SARSCoV2 antibody dynamics in blood donors and COVID19 epidemiology in eight Brazilian state capitals: A serial crosssectional study
Abstract
Background:
The COVID19 situation in Brazil is complex due to large differences in the shape and size of regional epidemics. Understanding these patterns is crucial to understand future outbreaks of SARSCoV2 or other respiratory pathogens in the country.
Methods:
We tested 97,950 blood donation samples for IgG antibodies from March 2020 to March 2021 in 8 of Brazil’s most populous cities. Residential postal codes were used to obtain representative samples. Weekly age and sexspecific seroprevalence were estimated by correcting the crude seroprevalence by test sensitivity, specificity, and antibody waning.
Results:
The inferred attack rate of SARSCoV2 in December 2020, before the Gamma variant of concern (VOC) was dominant, ranged from 19.3% (95% credible interval [CrI] 17.5–21.2%) in Curitiba to 75.0% (95% CrI 70.8–80.3%) in Manaus. Seroprevalence was consistently smaller in women and donors older than 55 years. The agespecific infection fatality rate (IFR) differed between cities and consistently increased with age. The infection hospitalisation rate increased significantly during the Gammadominated second wave in Manaus, suggesting increased morbidity of the Gamma VOC compared to previous variants circulating in Manaus. The higher disease penetrance associated with the health system’s collapse increased the overall IFR by a minimum factor of 2.91 (95% CrI 2.43–3.53).
Conclusions:
These results highlight the utility of blood donor serosurveillance to track epidemic maturity and demonstrate demographic and spatial heterogeneity in SARSCoV2 spread.
Funding:
This work was supported by Itaú Unibanco ‘Todos pela Saude’ program; FAPESP (grants 18/143890, 2019/215850); Wellcome Trust and Royal Society Sir Henry Dale Fellowship 204311/Z/16/Z; the Gates Foundation (INV 034540 and INV034652); REDSIVP (grant HHSN268201100007I); the UK Medical Research Council (MR/S0195/1, MR/V038109/1); CAPES; CNPq (304714/20186); Fundação Faculdade de Medicina; Programa Inova FiocruzCE/Funcap  Edital 01/2020 Number: FIO016700065.01.00/20 SPU N°06531047/2020; JBS – Fazer o bem faz bem.
Editor's evaluation
This article describes a large and compelling COVID19 serosurvey in Brazil that, when combined with death data, provides an estimate of the infection fatality ratio. This valuable study highlights both the strengths and challenges of blood donor serosurveillance in a pandemic environment where multiple waves of infection occur and immune responses wane relatively quickly.
https://doi.org/10.7554/eLife.78233.sa0Introduction
Brazil has experienced one of the world’s most significant COVID19 epidemics, with over 22 million cases and 621,000 deaths reported as of 14 January 2022. However, this national picture masks important subnational heterogeneity, with extensive variation in SARSCoV2 spread between population groups (Li et al., 2021) and locations (Castro et al., 2021; Hallal et al., 2020) as well as regional differences in the stringency of nonpharmaceutical interventions (de Souza Santos et al., 2021).
Understanding the drivers of these differences is crucial, both retrospectively as a means of evaluating past attempts at controlling spread, and as a guide to the potential impact of future transmission. Indeed, a significant fraction of the COVID19 burden in Brazil was driven by the emergence of the Gamma (P.1) variant of concern (VOC) in November 2020, which drove extensive resurgence of transmission following its apparent emergence in the Amazonas State capital city of Manaus. Despite the evidence of high levels of populationlevel immunity that should have hindered further transmission (Buss et al., 2021), a phenomenon attributed to the Gamma VOCs likely increased transmissibility and ability to partially evade immune responses (Faria et al., 2021). Subsequent spread to the rest of Brazil led to similar resurgence, extensive transmission, and disease burden leading to substantial pressure on health systems (Brizzi et al., 2021; de Oliveira et al., 2021; Martins et al., 2021). As with the first epidemic wave, the degree and extent to which different locations were affected varied markedly. Understanding the drivers of this variation is crucial to shed light on how and why SARSCoV2 spreads across different populations, and how past epidemics shape subsequent transmission of the virus. More generally, because previous natural infection may enhance vaccine response (Crotty, 2021; Reynolds et al., 2021; Stamatatos et al., 2021), understanding the extent of previous exposure in the country may have important implications for the development of epidemic waves driven by new variants in the context of the ongoing largescale, nationwide vaccination campaign.
Here, we analyse the divergent epidemic SARSCoV2 dynamics in eight of the biggest Brazilian cities (Belo Horizonte, Curitiba, Fortaleza, Manaus, Recife, Rio de Janeiro, Salvador, and São Paulo). We estimate the seroprevalence over time for these cities disaggregated by age and sex using repeated crosssectional convenience samples of routine blood donors collected from March 2020 to March 2021. We also provide estimates for the agespecific infection fatality rates (IFR, defined as the number of deaths per infection) and infection hospitalisation rates (IHR, the number of hospitalisations per infection) for these cities. In Manaus, the Gamma VOC became dominant before March 2021 (see Appendix 1—figure 1), enabling us to provide estimates of Gamma’s IFR and IHR. Our results highlight important differences in the drivers of SARSCoV2 epidemic spread across Brazil’s major population centres and underscore the utility of blood donors for regular serosurveillance as a tool to track progression of epidemics of emerging infectious diseases.
Methods
Selection of blood donors for estimation of seroprevalence
Each of the eight cities had a monthly quota of 1,000 kits for testing selected donation samples in this study. In order to select more representative samples, we selected blood samples so that the spatial distribution of residential location of selected donors matches the spatial distribution of population density in each municipality. More specifically, each city was divided into submunicipal administrative zones, and the original quota (1,000 kits) was divided into subquotas following the populational distribution of the city administrative zones. Starting from the second week of each month, we selected consecutive blood donors based on the geolocation of their residential postcode to fill the subquotas. In this way, donations with missing or wrong postal code were considered ineligible for selection. We chose the sample size (1,000) so an increase in crude seroprevalence of 5% can be detected with power $1\beta =80\%$ and confidence level $1\alpha =95\%$ assuming a baseline seroprevalence of 15%.
In Manaus, however, donor postcodes were not reliably collected, so that the number of missing and wrong values makes this strategy unfeasible. So, samples were selected consecutively with no postal code restrictions. We also developed a study management system to operationalize this sampling strategy, whereby blood donor postcodes and epidemiological data were automatically extracted and selected. After that, the selected donation sample IDs were released for the research assistant to be separated for testing.
From 453,211 available blood samples collected in all 8 cities except Manaus, 72,783 had a missing or invalid residential postal code, and 198,199 were from individuals living in regions not included in this study, thus 182,229 samples were eligible for selection. An average of 1010 samples were selected monthly for each city from March 2020 to March 2021, except for Recife where tests occurred until February 2021. A total of 104,013 samples were selected, but 6063 samples could not be retrieved or did not have enough volume to be tested, leading to 97,950 tested samples (951 samples per month in average for each city). Appendix 1—figure 2 contains a flowchart describing the selection procedure of blood donors.
In Brazil, blood donation samples are usually saved for 6 months, so when serological test kits were made available in July 2020, we could retrospectively select and test frozen samples from February to July. After this, period samples were selected and tested in real time. Antibody tests results were not made available to the blood donors themselves.
Blood donors are a convenience sample, and thus may not be representative of the wider population in terms of their risk of SARSCoV2 exposure. Appendix 1—figures 3–6 show a comparison between recorded blood donor demographics and the last available Brazilian census conducted in 2010. Donors differ systematically in age, sex, and selfreported skin colour compared to the population, but the income per capita is similar. To account for the differences in the agesex structure of blood donors, we divide donors in agesex groups and estimate the prevalence of each agesex group separately. Then, we calculate the seroprevalence of the population as a weighted sum of the seroprevalences of each agesex group.
SARSCoV2 serology assays
We applied chemiluminescent microparticle immunoassays (CIMA, AdviseDx, Abbott) that detect IgG antibodies against the SARSCoV2 nucleocapsid (N) because it was the only automated commercially available kit in Brazil when the study started (July 2020). We used this kit throughout the study until March in all eight cities except Recife, where we used the kit until February 2021. This assay suffers from signal waning  resulting in positivenegative transition, or ‘seroreversion’  during convalescence. This amounts to a fall in assay sensitivity through time. The Abbott antiN IgG CMIA shows particularly rapid signal decay when compared with other assays (Di Germanio et al., 2021). These antibody dynamics mean that as an epidemic progresses, the crude proportion of individuals with a positive test result will increasingly underestimate the true attack rate (Buss et al., 2021; Takahashi et al., 2021; Takahashi et al., 2020).
A test is considered positive if the obtained signal to cutoff (S/C) is greater or equal to a predefined threshold of 0.49. This is the lower threshold recommended by the manufacturer, which was used instead of the upper threshold of 1.4 to partially attenuate the effect of seroreversion. Appendix 1—figures 7–9 contain the number of tests disaggregated by month, age, sex and the monthly S/C distribution. We also decided to validate the results observed in Manaus, as this represents a unique sentinel population, by retesting all samples in November 2020 using the CIMA (AdviseDx, Abbott) that detects IgG antibodies against the SARSCoV2 spike (S) protein (see Appendix 1 for the validation analyses).
To determine the test sensitivity, we considered a cohort of 208 nonhospitalised symptomatic SARSCoV2 PCRpositive convalescent plasma donors tested within 60 days after symptom onset (Supplementary file 1). These donors had symptomatic COVID19 with PCRconfirmed SARSCoV2 infection and were recruited to provide convalescent plasma. We found a sensitivity of 90.6% for the antiN assay using a threshold of 0.49 S/C and 94.0% for the antiS assay. Specificity for the antiN assay was 97.5%, with 801 negative results in 821 prepandemic blood donation samples (Buss et al., 2021). Sensitivity and specificity for other assay thresholds are shown in Supplementary file 1. The antiS assay has a specificity of >99% (Di Germanio et al., 2021; Stone et al., 2021), and we assume 100% in this study. Although the sensitivity of both assays declines through time due to waning of the detected antibodies below the positivity threshold, the antiS IgG antibodies wane more slowly (Di Germanio et al., 2021; Stone et al., 2021). Sensitivity obtained from convalescent plasma donors is likely overestimated due to spectrum bias. This is because convalescent donors had moderatetosevere SARSCoV2 infection, and thus differ from the whole blood donor population (used to estimate seroprevalence), who are more likely to have had asymptomatic or mild disease.
We subsequently estimated the distribution of time to seroreversion, and thus the sensitivity decreasing through time, for the antiN assay. We first calculated this in the convalescent donors, in whom the date of symptom onset is known, and whose blood samples were collected longitudinally during convalescence. As such, the timetoseroreversion distribution was computed after accounting for right censoring. However, due to spectrum bias, the extrapolation of antibody waning from convalescent donors to whole blood donors is unlikely to be valid. As such, we obtained a second cohort of repeat blood donors in Manaus that provided multiple donations during the 2020–2021 period. These donors are expected to have the same antibody dynamics as the seroprevalence cohort, as they are drawn from the same population and have predominantly mild or asymptomatic infections. However, in this group the time of infection is unknown, as infection is inferred by serostatus alone. The procedure to manage this problem is described below.
Methods used to estimate the timedependent sensitivity
We developed an analytic method to correct raw seroprevalence data for seroreversion, improving on the method used in Buss et al., 2021. We first estimate the timetoseroreversion distribution using serial donations from repeat blood donors, which determines how sensitivity for a given individual decreases with the time after seroconversion. We then corrected the raw seroprevalence estimates for the changing sensitivity within a Bayesian framework. We first calculated attack rates for each age and sex group in each city and summed these using the proportion of each group in the Brazilian reference population to obtain standardised estimates. In this section, we describe a procedure to estimate the timedependent sensitivity used to obtain a seroprevalence estimate corrected for antibody waning.
Let ${\mathrm{s}\mathrm{e}}_{0}$ be the sensitivity measured shortly after symptomatic infection (i.e. the probability of an infected individual seroconverting to an S/C above the threshold), and ${p}^{+}\left[n\right]$ be the probability of a donor remaining positive $n$ weeks after seroconversion (given that the donor seroconverted). Then, the sensitivity of the test $n$ weeks after seroconversion is $\mathrm{s}{\mathrm{e}}_{0}\times {p}^{+}\left[n\right]$ for a given donor. In this section, we describe the procedure used to determine ${p}^{+}\left[n\right]$ from repeat blood donors data, for which time of infection and time of seroreversion are unknown. The seroreversion correction model described in the next section uses the estimate of ${p}^{+}\left[n\right]$ to calculate the seroprevalence accounting for seroreversion.
The criteria to select repeat blood donors were: (1) at least one positive test, indicating SARSCoV2 infection, (2) at least one subsequent blood sample, in order to interpolate the date of seroreversion, and (3) falling S/C between these two samples, because one of the samples used to define the interpolation curve may have occurred before the peak S/C; hence, the halflife and the date of seroreversion cannot be estimated. Therefore, all selected donors had at least one positive sample and at least one subsequent sample (positive or negative) with smaller S/C.
To calculate ${p}^{+}\left[n\right]$, we first estimate the date of seroreversion for each repeat blood donor using an exponential interpolation (a linear interpolation in the log scale). We choose an exponential interpolation because an exponential decay is frequently used to model antibody dynamics (Takahashi et al., 2021). When seroreversion is intervalcensored, i.e., a donor that has a positive test subsequently becomes negative, we interpolate an exponential curve that passes through the last positive sample and the first negative sample. Otherwise, when seroreversion is not intervalcensored, then it is rightcensored (a donor remains positive on their last sample), in which case we extrapolate an exponential line through the last two positive samples and project this forward. As such, the estimated instant of seroreversion for blood donor $i$ (denoted as ${{t}_{i}}^{}$) is the point where the interpolation curve crosses the threshold for a positive test. The interpolation procedure is illustrated in Appendix 1—figure 10. The proposed method may overestimate ${{t}_{i}}^{}$ if an S/C used to define the interpolation curve was sampled shortly after seroconversion before the peak S/C was reached, since in this case the S/C curve does not behave as an exponential, leading to an overestimated halflife. To partially overcome this problem, we discard donors that do not serorevert within 106 weeks (2 years) after their first positive test.
After estimating ${{t}_{i}}^{}$, for each blood donor $i,$ we compute the probability distribution of the date of seroconversion for that donor, ${p}_{i}$. For this, we identify the earliest and latest possible date of seroconversion $t}_{\text{min}$ (the date of the last negative result before seroconversion or 1 March 2020 if the donor has no positive results before seroconversion) and $t}_{\text{max}$ (the date of the first positive result). The relative probability of seroconversion within this window depends on the incidence of seroconversions due to SARSCoV2 infection for the cohort of repeat donors, denoted ${u}_{\text{repeat}}\left[n\right]$. To estimate this quantity, we calculate the histogram of the date of first positive donation for repeat blood donors and then apply a 30day moving average. As a sensitivity analysis, we also calculate ${u}_{\text{repeat}}\left[n\right]$ by computing the histogram of the date of onset of ion (SARI) deaths observed in Manaus, and applying to it a 7day window moving average, yielding similar seroprevalence estimates (Appendix 1—figures 11 and 12).
The distribution of the date of seroconversion is obtained by truncating the incidence curve of repeat blood donors ${u}_{\text{repeat}}\left[n\right]$ in the interval $\left[{t}_{\text{min}},{t}_{\text{max}}\right]$ and renormalizing the distribution. We then generate 1,000 samples of the instant of seroconversion ${t}_{i}^{+}\sim {p}_{i}\left[n\right]$ and compute the 1,000 sample delays between seroconversion and seroreversion $\Delta {t}_{i}={{t}_{i}}^{}{{t}_{i}}^{+}$.
The probability of the delay between seroconversion and seroreversion being $n\ge 1$ days (denoted as ${p}_{\text{day}}^{}\left[n\right]$) is calculated with the empirical histogram of the $1000\times {N}_{\text{donors}}$ samples of $\Delta {t}_{i}$ , $i=1,\cdots ,{N}_{donors}$. The distribution ${p}_{\text{day}}^{}\left[n\right]$ is then binned into weeks by taking the average of $\left({p}_{\text{day}}^{}\left[7n\right],\text{}{p}_{\text{day}}^{}\left[7n+1\right],\cdots ,{p}_{\text{day}}^{}\left[7n+6\right]\right)$ for $n\ge 1$. The resulting distribution, denoted as ${p}_{\text{week}}^{}\left[n\right]$, represents the probability of seroreversion exactly $n$ weeks after seroconversion.
Finally, the probability of a donor remaining positive $n$ weeks after seroconversion ${p}^{+}\left[n\right]$ (i.e. the probability of a donor seroreverting after week $n$) is obtained through,
The presented method is summarised in Appendix 1.
Estimating the seroreversion probability from convalescent plasma donors
Unlike repeat blood donors, convalescent plasma donors have a known date of symptom onset. To compute ${p}^{+}\left[n\right]$ for plasma donors, we estimate the instant of seroreversion for each plasma donor as described above and define the date of seroconversion as 8 days after the reported date of symptom onset. This interval of 8 days is the average lag between seroconversion and seroreversion reported in Orner et al., 2021 for a threshold of 1.4 S/C, but it can be shorter for a threshold of 0.49 employed in this work. The probability mass function of the time to seroreversion ${p}_{\text{day}}^{}\left[n\right]$ is then the empirical histogram of $\Delta {t}_{i}={{t}_{i}}^{}{{t}_{i}}^{+}$, and ${p}^{+}\left[n\right]$ is obtained from ${p}_{\text{day}}^{}\left[n\right]$ using the method presented above.
Our proposed seroreversion correction model
Here, we present a Bayesian model that draws posterior samples from the incidence over time corrected by sensitivity, specificity, and seroreversion using as input the estimated curve for ${p}^{+}\left[n\right]$, the number of weekly positive tests, and total number of tests. Even though the main output of the model is the incidence at week $n$ for agesex group $a$ (denoted as $u[n,a]$), the seroprevalence at week $n$ for group $a$ can be calculated from $u[n,a]$ as $\rho \left[n,a\right]={\sum}_{k=1}^{n}u[k,a]$. For simplicity, the proposed model ignores the delay between infection and seroconversion, as it should have small impact on the estimate of $u[n,a]$. To define the agesex groups, age was discretized in the intervals 16–24, 25–34, 35–44, 45–54, and 55–69.
Assuming that the sensitivity $\mathrm{s}{\mathrm{e}}_{0}$ and specificity $\mathrm{s}\mathrm{p}$ of the assay are independent of the agesex group, the probability of a random person from agesex group $a$ being tested positive at week $n$, denoted as $\theta [n,a]$, is
The derivation of the expression above is presented in Appendix 1. The left term $\mathrm{s}{\mathrm{e}}_{0}{\sum}_{k=1}^{n}{p}^{+}[nk]u[k,a]$ represents true positives (previously infected donors that are still seropositive), while the right term $\left(1\mathrm{s}\mathrm{p}\right)\left(1{\sum}_{k=1}^{n}u[k,a]\right)$ represents false positives (uninfected donors that test positive).
Let us denote as ${T}^{+}[n,a]$ and $T\left[n,a\right]$, respectively, the number of positive tests and the total number of tests for week $n$ and agesex group $a$. Given $\theta [n,a]$, the probability distribution of ${T}^{+}[n,a]$ is
We use a Bayesian framework to draw posterior samples from $u$ assuming a noninformative prior, but limiting the final seroprevalence in the interval $[0,b]$, where $b$ is a fixed input of the algorithm that can be 1 or 2 depending on whether reinfections are allowed, and we use $b=2$ in this work. Instead of defining a prior distribution for $u[n,a]$ directly, we decompose it into $u\left[n,a\right]={\rho}_{\text{max}}\left[a\right]{u}_{\text{norm}}\left[n,a\right],$ where ${\rho}_{\text{max}}\left[a\right]\sim \mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\left(0,b\right)$ sets the upper bound of the final prevalence to $b$ and ${u}_{\text{norm}}\left[:,a\right]\sim \mathrm{D}\mathrm{i}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{h}\mathrm{l}\mathrm{e}\mathrm{t}\left(1,1,\dots ,1\right)$ is the normalised incidence which sums to 1. This decomposition is equivalent to assuming a uniformly distributed prior for $u\left[:,a\right]$ in the simplex $0\le {\sum}_{n=1}^{N}u\left[n,a\right]\le b$ with $u\left[n,a\right]\ge 0\forall n$.
After drawing posterior samples from $u[n,a]$, we calculate the seroprevalence at week $n$ for agesex group $a$ as $\rho \left[n,a\right]={\sum}_{k=1}^{n}u[k,a]$ and then compute the agesex weighted seroprevalence $\rho \left[n\right]$, given by
where $\mathrm{p}\mathrm{o}\mathrm{p}\left[a\right]$ is the population for the agesex group $a$ in the corresponding city and $M$ is the number of agesex groups. Of note, in this work we also refer to $\rho [n]$ as the estimated seroprevalence, cumulative seroprevalence or attack rate.
The presented Bayesian model is summarised in Appendix 1. The posterior samples are drawn using a MonteCarlo Markov Chain algorithm with 100,000 iterations.
The incidence returned by the model was validated through posterior predictive checks by randomly selecting 1,000 samples from $u\left[n,a\right]$ and drawing samples from ${T}^{+}\left[n,a\right]\mid \theta \left[n,a\right]\sim \mathrm{B}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{a}\mathrm{l}\left(T\left[n,a\right],\theta \left[n,a\right]\right)$ . The resulting crude seroprevalence is then compared with the measured crude seroprevalence (Appendix 1—figure 13).
It is worth noting that the agespecific crude seroprevalence can be larger than the seroprevalence corrected for seroreversion in some weeks, as the model may remove outlier samples. This is because seroprevalence curves that cannot be reconstructed by the model (e.g. due to bias or sampling noise) generate a small likelihood, hence, a smaller probability of being included in the set of posterior samples generated by the model. Therefore, the model excludes weeks where donors are significantly biased towards more seropositive or more seronegative individuals.
The proposed Bayesian seroreversion correction model can be seen as an improvement on that presented in Buss et al., 2021. The model in Buss et al. assumed a parametric form for time to seroreversion and derived the parameters by assuming an increasing cumulative seroprevalence in the repeated crosssectional samples of blood donors in Manaus. Here, we derived the distribution directly from repeat blood donors without assuming any parametric form. Also, Buss et al. applied the seroreversion correction method to the measured seroprevalence corrected for sensitivity, specificity, and reweighted by age and sex, while here we estimate the seroprevalence in each age group separately, allowing the identification of nonhomogeneous incidence in different age groups.
Despite these differences, the results presented here are compatible with the seroprevalence estimates of 28.8 and 76.0%, respectively, for São Paulo and Manaus in Buss et al. The proposed seroreversion method also differs from other methods in the literature (Shioda et al., 2021; Takahashi et al., 2021) in that we use the incidence curve to estimate the timedependent sensitivity instead of the deaths or confirmed cases curve, producing a seroprevalence that does not depend on case reporting and that can be reliably inferred in epidemics where the IFR changes with time, as was the case in Manaus.
Estimating the IFR for December 2020
We estimate the IFR using total deaths due to Severe Acute Respiratory Infection (SARI), which includes PCR and clinically confirmed SARSCoV2 infection as well as SARI deaths without a final diagnosis, and we exclude SARI deaths confirmedly caused by other aetiologies. This approach reduces underreporting, particularly in 2020 when testing was not widely available, as discussed in de Souza et al., 2020. We further justify this approach in Appendix 1.
We retrieved the daily number of SARI deaths from SIVEPGripe (Sistema de Informação da Vigilância Epidemiológica da Gripe), a public database containing individuallevel information of all SARI cases reported in Brazil. To estimate the IFR in 2020, we use the seroprevalence estimated by our model for 16 December 2020 and select only SARI deaths with symptom onset between 1 March and 15 December 2020. Selecting deaths based on the date of first symptoms instead of date of death was possible because SIVEPGripe contains the date of symptom onset for each individual. For the first wave of COVID19 that occurred in the eight cities, we estimate the number of cases as the agespecific population size (https://demografiaufrn.net/laboratorios/lepp/) multiplied by the estimated seroprevalence in the corresponding age group. We propagate the uncertainty in the prevalence estimate through the calculation of IFR.
Let $\rho \left[a\right]$ and $\mathrm{p}\mathrm{o}\mathrm{p}\left[a\right]$ be the cumulative seroprevalence and the population estimated for age group $a$. We assume a uniform distribution in the interval [0, 1] as a noninformative prior for $\mathrm{I}\mathrm{F}\mathrm{R}\left[a\right]$, and the number of deaths $D\left[a\right]$ observed for each age group $a$ is Binomialdistributed with size $\lfloor \rho \left[a\right]\times \mathrm{p}\mathrm{o}\mathrm{p}\left[a\right]\rfloor $ (the number of infections) and probability $\mathrm{I}\mathrm{F}\mathrm{R}\left[a\right]$. For each sample of $\rho \left[a\right]$, we draw a sample of the posterior distribution of $\mathrm{I}\mathrm{F}\mathrm{R}\left[a\right]$ , given by
and compute the median, interquartile ranges (IQRs), and 95% confidence intervals of the IFR by retrieving the quantiles of the posterior distribution.
To infer the IFR, we considered the age groups 16–24, 25–34, 35–44, 45–54, and 55–64. We applied the same method to estimate the overall IFR but using a single age group containing all individuals aged between 16 and 64. Therefore, IFR of individuals older than 64 or younger than 16 is not included in the overall IFR estimates. The method used to infer the IFR was also applied to compute the infection hospitalisation rate (IHR), but we used the number of hospitalisations with SARI instead of the number of deaths.
We note that the proposed seroreversion correction model can be used to estimate the attack rate and IFR of epidemics driven by other lineages in other regions. However, the uncertainty of the seroprevalence estimate increases over time, as a larger amount of seroreversion needs to be corrected. Therefore, estimated attack rates and IFRs suffer from larger uncertainty when longer time periods are considered.
To validate the obtained IFRs, we also estimate the IFRs using the measured prevalence corrected only by the sensitivity and specificity of the assay, without explicitly accounting for seroreversion. In this validation analysis, we use a small threshold of 0.1 S/C to avoid underestimating the prevalence due to seroreversion (see Appendix 1).
Estimating the IFR for the Gamma VOC
We estimate the IFR and the attack rate separately for the second, Gammadominant, SARSCoV2 wave that occurred in Manaus. The Gamma variant was first detected in Manaus in November 2020, and its prevalence among PCRpositive patients grew rapidly to 87.0% on 4 January 2021 (Faria et al., 2021). For this reason, it is reasonable to assume that all infections in Manaus that occurred after 15 December, 2020, are due to the Gamma VOC. The Gammadominated wave was characterised by a nonnegligible proportion of reinfections (Coutinho et al., 2021; Faria et al., 2021; Prete et al., 2022). It is estimated that 13.6–39.3% of the infections in the second wave of COVID19 epidemic in Manaus were reinfections (Prete et al., 2022), which are explained by the higher invitro reinfection potential of Gamma (Lucas et al., 2021) and partial immunity waning 8 months after the first surge. Thus, to calculate the attack rate and IFR of the Gammadominated wave, reinfections must be considered.
However, estimating the incidence of reinfections among positive donors is not straightforward  as a positive result may be either primary infection or reinfection, and these cannot be distinguished using a single test result. For this reason, it was not possible to obtain a point estimate for the number of infections that happened in the second wave in Manaus. To overcome this problem, we calculate upper bounds for the attack rate of the Gammadominated wave in Manaus (i.e. the incidence between December 2020 and March 2021) and conversely lower bounds for the IFR of the Gamma VOC.
We first estimate the attack rate of the second wave using a Bayesian model that does not take reinfections into account. This model also neglects seroreversion for individuals infected during the second wave due to the small interval of 3 months considered in this analysis (see Appendix 1 for a complete description of the model). Denoting as $\hat{\mathrm{A}\mathrm{R}}$ the attack rate estimated by this model, the true attack rate $\mathrm{A}\mathrm{R}$ is given by $\mathrm{A}\mathrm{R}=\hat{\mathrm{A}\mathrm{R}}+R+S$, where $R$ is the proportion of donors that were seropositive in December 2020 and subsequently had a reinfection, and $S$ is the proportion of donors that were seropositive in December 2020 and became seronegative in the following months. Since $R+S$ cannot be greater than the seroprevalence in December 2020 (denoted as ${\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}}$), the upper bound for the attack rate is $\mathrm{A}{\mathrm{R}}_{\mathrm{m}\mathrm{a}\mathrm{x}}=\hat{\mathrm{A}\mathrm{R}}+{\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}}$. Therefore, the upper bound is obtained assuming that all individuals that were seropositive in December were later reinfected or were seronegative in March 2021.
To estimate $\mathrm{A}{\mathrm{R}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$, we compute the monthly number of positive tests ${T}^{+}\left[n\right]$ from December 2020 to March 2021 for each agesex group, as well as the number of true positives (TP) and false negatives (FN) from convalescent plasma donors and the number of false positives (FP) and true negatives (TN) from the prepandemic blood donors cohort in Manaus (Supplementary file 1). The Bayesian model generates posterior samples of the crude monthly incidence and the crude seroprevalence in December ${\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}}$ . We then correct the crude incidence by the sensitivity of the assay to obtain posterior samples of $\hat{\mathrm{A}\mathrm{R}}$, which are then added to the posterior samples of ${\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}}$, resulting in samples of $\mathrm{A}{\mathrm{R}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$. As explained above, the lower bound for the IFR is then calculated using the upper bound of the attack rate and the number of deaths with symptom onset between 16 December and 15 March. This procedure is repeated for each agesex group independently and is summarised in Appendix 1.
Only small estimates of the upper bound for the attack rate are informative, as in scenarios where ${\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}}$ is small. To limit ${\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}}$, we estimate the incidence using a threshold of 1.4 S/C (the upper threshold recommended by the manufacturer) instead of 0.49 S/C (the lower threshold recommended by the manufacturer) and correct for sensitivity based on 163 true positives and 30 false negatives in the plasma donors cohort. Since the specificity of the test using a threshold of 1.4 is 99.9%, and since it is not straightforward to take the specificity into account when reinfections are allowed, we do not correct for specificity in this analysis.
We additionally computed the IFR obtained using the seroprevalence estimated by the model. It is worth noting that our seroreversion correction model only estimates the incidence among seronegative individuals, thus an S/C boosting due to reinfection is not detected by our method. As such, our model estimates the seroprevalence assuming there are no reinfections among positive individuals, underestimating the size of the second wave in Manaus.
The IHR for the Gamma VOC was estimated using the same procedure but using the number of hospitalisations by SARI instead the number of deaths.
This method can be applied to estimate upper bounds for the attack rate of epidemics driven by other lineages with high rates of reinfection such as Delta and Omicron VOCs, but as previously highlighted the upper bound is only informative if the initial crude seroprevalence is small. This may not be the case in regions where vaccines inducing antiN antibodies were applied, as it is not possible to distinguish vaccination from natural infection based only on antiN serological data.
Definition of the homestay index
The homestay index for the eight cities was extracted from https://bigdatacovid19.icict.fiocruz.br/. It was calculated using data from Google Mobility reports using the procedure described in Barreto et al., 2021. The homestay index is defined as
where ${X}_{H},{X}_{G},{X}_{P},{X}_{T},{X}_{R}$, and ${X}_{W}$ are, respectively, the variation of mobility (using prepandemic mobility levels as baseline) in the following place categories: residential areas, grocery and pharmacy, parks, transit stations, retail and recreation, and workplaces.
Calculation of agestandardised estimates
In this work, we calculated the agestandardised mortality, the agestandardised overall IFR, and the agestandardised overall IHR. The procedure used to perform age standardisation was the same for all these quantities. We define an agestandardised variable as the estimate that would be obtained if all cities had the same age structure. Denoting $\eta \left[a\right]$ as an agespecific IFR or IHR for a given city and $w\left[a\right]$ as the proportion of the combined population of all eight cities belonging to age group $a$, then the agestandardised overall IFR or IHR is $\sum _{a=1}^{M}w\left[a\right]\eta \left[a\right],$ where $M=5$ is the number of age groups. Similarly, denoting $\mu (t,a)$ as the mortality for age group $a$ and day $t$ for a given city, the agestandardised mortality is $\sum _{a=1}^{M}w\left[a\right]\mu (t,a).$
Results
Serology assay validation and antibody waning
Antibody kinetics vary with disease severity (Buss et al., 2021; Lumley et al., 2021; Takahashi et al., 2021), and whole blood donors represent predominantly asymptomatic or mild SARSCoV2 infections due to donation eligibility criteria (Buss et al., 2021). As such, we sought to estimate a timetoseroreversion distribution that accurately reflected the blood donor convenience sample used in this study. We identified and tested 7675 repeat whole blood donors in Manaus who had made multiple donations throughout for 2020–2021 (Appendix 1—figure 14) and used these data to estimate the timetoseroreversion probability distribution (see Materials and methods).
The results are shown in Figure 1, which compares the halflife, peak S/C values, and timetoseroreversion of repeat whole blood donors to the cohort of symptomatic convalescent plasma donors used to determine sensitivity. Repeat blood donors had a shorter assay signal halflife than plasma donors (median [IQR] 69.3 [53.0–103.8] versus 105.9 [62.7–185.1] days) and a lower observed peak S/C ratio (median [IQR] 2.89 [1.49–4.83] versus 5.08 [3.22–6.99]), yielding a shorter median time between seroconversion and seroreversion (203 [147–294] days versus 280 [175–441] days). This highlights the importance of choosing a timetoseroreversion distribution that is appropriate for the use case  the rate of waning seen in PCRconfirmed symptomatic disease would have resulted in underestimation of SARSCoV2 attack rates.
COVID19 mortality across Brazilian capitals
The location of the eight Brazilian state capitals that contributed serology data is shown in Figure 2A. They collectively represent approximately 14% of the total Brazilian population. The age distributions of the eight cities differ widely (Figure 2—figure supplement 1), as such COVID19 mortality is presented as agestandardised rates (see Appendix 1—figure 15 for the crude mortality curves). Between 1 March 2020 and 31 March 2021, the agestandardised mortality rate varied from 1.7 deaths per 1,000 inhabitants in Belo Horizonte to 5.3 deaths per 1,000 in Manaus, which had twice the mortality of Fortaleza, the city with the next highest mortality (Figure 2C).
Figure 2B shows the homestay index for the eight cities (see Materials and methods for the definition). Manaus, the city with the youngest population, returned to prepandemic levels of mobility by July 2020, having consistently lower homestay index (i.e. higher mobility) than other cities after June 2020, whereas the other seven cities showed a relatively homogenous mobility pattern. The shape of the mortality curves also varied markedly (Figure 2D). Manaus was also an outlier in having the lowest income per capita, health insurance coverage, and lowest proportion of the population with comorbidities, along with the highest number of residents per household (Figure 2—figure supplement 2).
Blood donor serosurveillance
Using an average of 951 monthly samples of routine whole blood donations (from March 2020 to March 2021, a total of 97,950 samples) in each of the eight cities, we measured the crude seroprevalence of antiN IgG antibodies detectable by the Abbott CIMA (Table 1). However, these raw estimates of seroprevalence are affected by seroreversion dynamics and provide a poor guide for assessing past levels of population exposure.
Using our Bayesian seroreversion correction model, we present in Figure 2D the agestandardised SARSCoV2 attack rates (i.e. the cumulative rate of the population that was infected or reinfected) as of March 2021 after accounting for test sensitivity, test specificity, and IgG seroreversion (coloured lines) along with the directly measured seroprevalence (light grey boxplots) and the estimated seroprevalence adjusting for test sensitivity and specificity (dark grey boxplots). Our results further underscore the significantly different scales of SARSCoV2 epidemic impact experienced across the eight cities, with the implied attack rates ranging from only 19.3% in Curitiba, to as high as 75.0% in Manaus by December 2020 (see Table 1). Alternative cumulative seroprevalence estimates produced using different timetoseroreversion distributions are similar to those in Figure 2D and shown in Appendix 1—figure 12. We note that even though the seroprevalence estimated by our model includes reinfection in seronegative individuals, the model does not capture reinfection in already positive individuals. Therefore, the model is likely to underestimate SARSCoV2 attack rates in scenarios where reinfection is not rare, and the obtained seroprevalence can surpass 100% due to reinfections among seronegative individuals.
The slope of the seroprevalence curves (Figure 2D) also differed significantly across cities, showing different dynamics of antibody acquisition at the population level according to the shape and dynamics of the epidemic experienced. Cities with only minimal epidemic peak as Belo Horizonte and Curitiba showed near constant rates of increase in seropositivity after adjustment for antibody waning. By contrast, cities with substantial epidemic peak as Fortaleza and Manaus demonstrated significant variation in the rate at which estimated seropositivity increased in the population, with these rates highest during the epidemic peaks. These findings highlight the capacity of blood donorbased serological data to recapitulate important temporal trends in the intensity and dynamics of the epidemics across these eight cities.
The estimated seroprevalence in June and July in Fortaleza was significantly smaller than the measured seroprevalence without correction for seroreversion, even though the seroprevalence estimates disaggregated by age and sex (Appendix 1—figure 16) lie within or above the confidence intervals of the measured seroprevalence. This effect happened especially in women, which had a crude seroprevalence that was significantly larger than in men in June and July 2020, but became similar in the following months. It is possible that the seroreversion rate observed in Fortaleza had been faster than the rate estimated from repeat blood donors, in which case we undercorrected for seroreversion, underestimating the attack rate. However, a more likely explanation is that samples between March and July 2020 for Fortaleza are less representative of the population, since only 39.4% from 4970 selected samples could have been retrieved and tested, compared to 97.0% for the other cities and months. As such, seropositive individuals from Fortaleza may have been more likely to donate in these months, leading to an overestimated crude seroprevalence.
Agesex patterns in blood donor seroprevalence
We next examine the patterns and dynamics of attack rates across different groups by disaggregating the seroprevalence data by age and sex. The seroprevalence estimates disaggregated by age and sex are shown in Figure 3 (see Appendix 1—figures 17–18 for seroprevalence disaggregated by only age or sex). Across the eight cities, our results consistently show differences between sexes  on average, men tended to have higher attack rates than women, although the degree and extent of this difference varied between cities. In São Paulo, the seroprevalence in December 2020 for men was 30.6% compared to the 23.0% estimated in women (i.e. 33.5% (95% CrI 17.7–51.9) higher, Figure 3B). By contrast, seroprevalence in Curitiba in December 2020 was similar for women and men, being only 4.65% (95% CrI –11.5 to 18.5) higher in women.
We also observed an extensive variation in the dynamics of populationlevel seroprevalence between age groups, with seroprevalence in December 2020 typically highest in younger age groups. The seroprevalence of individuals below the age of 55 increased in all cities except for Recife when compared to donors aged between 55 and 69, increasing by 34.1% (95% CrI –2.23–91.2) in Curitiba and decreasing by a small factor of 0.5% (95% CrI –24.8–19.1) in Recife. Furthermore, in cities with a large increase in seroprevalence during the first epidemic wave (i.e. Manaus, Recife, Fortaleza, and Salvador), this was primarily driven by younger men. In these locations, the differences between agesex groups slowly narrowed during the long period of less intense transmission (Figure 3A). This highlights important differences between agegroups in the extent to which they were exposed to the virus and/or contributed to transmission at different points during the regional epidemics  differences that are not evident, or certain, from case or death counts alone.
In addition to the differences in attack rates by age and sex, seroprevalence did not increase homogeneously among different age and sex groups. In Manaus, seroprevalence was significantly larger in men and younger individuals aged 16–44 in July 2020, but between July and December seroprevalence increased faster in women and donors older than 45 years, leading to smaller differences in attack rate by age and sex in December 2020 (Figure 3B). Similar patterns are also observed in Salvador, Recife, and Fortaleza, although with smaller age and sex inequalities.
Variation in the SARSCoV2 IFR across age groups and locations
Using estimates of the cumulative number of individuals infected alongside records of COVID19 deaths available from Brazil’s SIVEPGripe platform, we next calculated the IFR for each city and age group. Figure 4A presents the estimated agespecific IFRs for each municipality as of December 2020, before the Gamma VOC epidemic in Brazil. Our results show the IFR significantly increases with age, ranging from 0.03% in individuals aged 16–24 years to 1.31% in individuals aged 55–64 years. This is inkeeping with previous work highlighting a strong age dependency in COVID19 mortality (Brazeau et al., 2020; Buss et al., 2021; O’Driscoll et al., 2021). Cities presented different agestandardised overall IFRs, being smaller in Manaus (0.24%) and higher in Curitiba (0.54%).
There was a strong correlation (Pearson’s correlation = 0.92) between the agestandardised mortality rate in each city and the attack rate inferred from blood donor serosurveillance data (Figure 4B). Both the overall IFR and the overall IFR adjusted for the age structure of the city differed significantly between cities (Figure 4C), showing that the IFR differences cannot be explained only by the different age structures. Despite the differences between cities, the obtained agespecific IFRs were similar to the estimates from Brazeau et al., 2020 but higher than the estimates from O’Driscoll et al., 2021 (Figure 4D). The agespecific and overall IHR were also estimated (Figure 4—figure supplement 1) and showed similar patterns, being larger in Belo Horizonte, Curitiba, and São Paulo.
The obtained IFRs and attack rates for December 2020 were validated using alternative approaches that do not correct directly for seroreversion, not depending on the proposed seroreversion correction model (see Appendix 1).
The dynamics and epidemiological impacts of the Gamma VOC in Manaus
As previously highlighted, we could not obtain a point estimate of the attack rate in the Gammadominated period in Manaus because we are unable to identify which of the seropositive blood donors are primary infections and which are reinfections. Instead, we calculated upper bounds assuming maximum proportions of reinfections. The inferred upper bound of the agespecific attack rate in the Gammadominated period in Manaus ranged from 30.6% (95% Bayesian CrI 22.8–41.1) to 46.0% (95% CrI 32.8–60.6) in individuals aged 45–54 and 55–64 (Figure 5—figure supplement 1), showing small variation among age groups. The estimated upper bound for the agestandardised cumulative attack rate in the second period dominated by the Gamma variant was 37.5% (95% CrI 35.3–42.6), significantly smaller than the cumulative attack rate of 75.0% (Figure 2) estimated for the first period dominated by nonGamma variants.
Comparing to the COVID19 attributable hospitalisations and deaths reported to the SIVEP database, we next used the estimated upper bounds of the agespecific attack rates in the Gamma period in Manaus to calculate lower bounds of the agespecific IHR and IFR for the Gamma period. We then compared the IFRs and IHRs obtained with the attack rate estimated for the period during which nonGamma variants dominated (from 1 March 2020 to 15 December 2020). The resulting agespecific IFRs and IHRs are shown in Figure 5A, B, respectively, and the relative risks obtained using the IFR or IHR in December 2020 as baseline in Figure 5C, D. The lower bound for the IHR increased in all age groups, from 34.4% (95% CrI 6.5–70.0) in individuals aged 16–24 to 163.4% (95% CrI 90.9–264.3) in individuals aged 45–54 when compared to the IHR estimated for the nonGamma period. The increased hospitalisation risk combined with an increased inhospital fatality rate (HFR, defined as the number of deaths per hospitalisation) during the second wave (Appendix 1—figure 19) resulted in an increased agespecific IFR, with a lower bound increasing 93.8% (95% CrI 36.4–186.4) in individuals aged 55–64 to 273.5% (95% CrI 167.8–423.4%) in individuals aged 45–54 when compared to the first wave (Figure 5C). As such, even though the IFR and IHR increased for all age groups during the Gammadominated period, this difference was more significant in younger age groups. The obtained lower bound for the overall IFR was 0.527% (95% CrI 0.447–0.630), 2.91 (95% CrI 2.43–3.53) times higher than the estimated IFR for the first wave in Manaus.
Discussion
Our results highlight the divergent epidemic dynamics across eight of Brazil’s biggest cities as reflected by mortality rates, and show that these differences are recapitulated in blood donorbased serial crosssectional serosurveillance. Despite the large IFR differences observed across cities, seroprevalence was strongly correlated with cumulative agestandardised mortality (Figure 4B). These results reinforce the validity of blood donors as a convenient population for serosurveillance. A previous study (Mina et al., 2020) has highlighted the need for a reliable, costeffective method of immunological surveillance to provide evidence of past infection and to understand the dynamics of emerging disease. Even though serology is less precise for identifying infections on an individual level, it is an effective tool for monitoring epidemics at a population level. As blood donation programs are an existing component of medical infrastructure globally and in which blood samples are readily available in many locations, this approach can be rapidly implemented and carried out in large populations.
We estimated larger attack rates in individuals aged 16–54 years. This is consistent with previous work examining age patterns of transmission from mobility data in the United States (Monod et al., 2021), but we have measured infection directly rather than making inferences indirectly on the basis of COVID19 deaths and movement. Possible reasons for the higher attack rate in people aged 16–54 years include, but are not limited to, different risk perception and shielding practises, and disease biology with more frequent asymptomatic infections in younger people, which increase infection risk in this age group due to greater mixing among working age adults. We also found overall higher levels of seroprevalence in men compared to women, and these patterns changed over time. For instance, in Manaus, a very high seroprevalence was reached rapidly among young men by July 2020, after which relatively little increase in overall seroprevalence occurred in men. By contrast, among older women, who reached less than half the attack rate seen in men by June, the seroprevalence continued to increase. This heterogeneity in transmission in a location with high overall antibody prevalence meant that some groups remained relatively susceptible and perpetuated transmission at a lower level (Buss and Sabino, 2021; Lalwani et al., 2021). Other works suggest that socioeconomic condition also contributed to heterogeneity of SARSCoV2 spread in Manaus (Lalwani et al., 2021), which is confirmed by the large seroprevalence observed in Black and lesseducated donors (Appendix 1—figure 20).
We also confirm a strong age dependency of COVID19 IFRs (Brazeau et al., 2020; O’Driscoll et al., 2021). Although agespecific IFRs were roughly similar across the cities (Figure 4A) and similar to estimates in the literature (Figure 4D), there were some noticeable differences. For example, the more affluent south and southeastern cities of Belo Horizonte, Curitiba, and São Paulo tended to have higher agespecific IFRs, whereas in the northern and northeastern cities of Manaus, Salvador, and Fortaleza, the agespecific IFRs tended to be lower. This may be due to underreporting of deaths but might also reflect lower prevalence of comorbidities in the latter populations (Figure 2—figure supplement 2). Cities with larger IFRs also had larger IHRs, suggesting that the differences in IFR reflect the different risks of developing a severe disease. The different lineages circulating in the eight cities may have also contributed to the observed IFR and IHR difference (Appendix 1—figure 1). While most of the cases in the first wave in Amazonas and Ceará were caused by earlier lineages, the lineages B.1.1.28, B.1.1.33, and later P.2 (Zeta) were more prevalent in other states. It is worth noting the IHR also depends on the probability of an individual with severe disease being hospitalised. This probability depends on access to health facilities and availability of healthcare resources, and therefore may vary across cities even if disease severity remains constant.
Our results also clearly demonstrate a higher IHR during the Gammadominated observation period compared to the nonGamma observation period in Manaus for all age groups (Figure 5). This supports observations (Banho et al., 2021) that the Gamma VOC tends to cause more severe disease than the ancestral nonGamma variants circulating locally, even among young adults in Manaus. The larger increase in IHR for younger adults aged 25–54 years is compatible with the younger profile of hospitalisations of the Gammadominated wave in Brazil (de Souza et al., 2021)^{,} observed before vaccination coverage reached significant levels in older age groups. In Manaus, the increased levels of hospitalisation caused parts of the healthcare system to collapse during the second wave causing an increase in HFR as previously described (Brizzi et al., 2021), further increasing the IFR. The higher IFR associated with Gamma VOC infection during the second wave is therefore due to a combination of two factors – increased disease severity resulting in a greater proportion of infections requiring hospitalbased care (the IHR, arising primarily from intrinsic viral properties and pathogenicity), and the impacts of this increased healthcare pressure on mortality withinhospitals (the HFR, arising primarily from healthcare pressure).
There are some relevant limitations to our results that need to be pointed. First, blood donors are a convenience sample, and extrapolation to the entire population should be done with caution. Due to eligibility criteria in Brazil, blood donors are limited to those aged 16–69 years, with a strong skew towards younger adults even within this eligibility range (Figure 2—figure supplement 1) in most Brazilian regions. However, our results do suggest that blood donor serosurveillance agrees with other metrics of epidemic size as mortality, both cumulatively (Figure 5B) and through time (Figure 3). Moreover, both sensitivity and seroreversion could be an agedependent process as a proxy for disease severity, i.e., older individuals are more likely to be symptomatic, seroconvert, and have longer time to seroreversion. Indeed, we see this pattern of longer halflives and larger peak S/Cs in convalescent plasma donors who had recovered from more severe disease (Appendix 1—figure 21). Therefore, correction of crude seroprevalence for antibody waning could possibly be confounded by demographic differences between the eight cities. However, since individuals that had a severe disease are unlikely to donate blood, seropositive whole blood donors are likely fairly homogenous in having had milder or asymptomatic disease, and as such, the rate of waning may not vary significantly between locations. An additional important point to note is that the longer an epidemic last, the more frequent reinfections become due to the natural waning of immunity in the time period following infection. Our data span over a year of transmission in areas with multiple waves with high SARSCoV2 burden and consequently nonnegligible reinfection rates, as such it is difficult to reliably infer the attack rates from seroprevalence data towards the end of the time series. For this reason, our model produces upper bounds for cumulative prevalence of >100% in Manaus by early 2021.
Despite these limitations, blood donors represent an accessible population to detect trends of the epidemic that otherwise could only be obtained through expensive populationbased studies, which are difficult to establish in Brazil during the course of a rapidly progressing epidemic. Studies to understand the main differences between blood donors and the general population would help the development of better sampling protocols to mitigate bias and should be part of preparedness for future epidemics of infectious diseases.
Appendix 1
Validation of the obtained attack rates and IFRs
The seroprevalence and IFRs obtained in December 2020 estimated with our seroreversion correction model were validated using a smaller threshold of 0.1 and correcting only for sensitivity and specificity, without explicitly correcting for seroreversion (Appendix 1—figure 22, Supplementary file 1). Even though this approach underestimates the seroprevalence (thus overestimates the IFR) because a fraction of previously seropositive donors had already seroreverted by December 2020 (leading to a significant number of false negative test results), the obtained attack rates and IFRs were similar to the estimates of our model. The inferred seroprevalence for Manaus and Curitiba in December 2020 was, respectively, 61.0% (95% CrI 56.5–65.4%) and 13.4% (95% CrI 10.0–17.2%), compatible with the estimates of our seroreversion correction model (Figure 2, Table 1) given that these quantities underestimate the seroprevalence due to waning. The IFR pattern across cities was also similar in this analysis, being higher in Curitiba and smaller in Manaus for almost all age groups.
An alternative approach to estimating the attack rate in December 2020, in the face of waning antibodies and falling assay sensitivity, is to calculate the IFR early in the epidemic, prior to significant waning, and extrapolate the number of future cases from the reported death time series. To further validate the attack rates, we calculated the agespecific IFRs in June 2020 (when less seroreversion is expected) for the age range eligible to donate blood and extrapolated using only the deaths within this age bracket. As such, the seroprevalence obtained for the other months is based solely on the number of deaths and the IFR inferred for June 2020 (Appendix 1—figure 23). This approach led to an estimated seroprevalence of 90.8% (95% CrI 78.1–107.7%) and 10.9% (95% CrI 1.2–28.0%) in Manaus and Curitiba, respectively, in December 2020, which are compatible with our estimates if confidence intervals are considered. Nevertheless, this approach has the limitation of assuming a constant IFR through time and only using a small amount of the total available serologic data.
To validate the inferred cumulative attack rate in November 2020 prior to the Gammadominated second wave and also in April 2021, following this second wave, we retested 996 samples from November 2020 in Manaus and tested 769 samples from April 2021 using the Abbott antiS SARSCoV2 IgG CIMA (Appendix 1—figure 24), which showed less waning than the Abbott antiN assay used in this work (Stone et al., 2021). As such, the usage of the antiS assay reduced the difference between the seroprevalence obtained without explicitly correcting for seroreversion and the true seroprevalence. A sensitivity of 94.0% was obtained by testing convalescent plasma donors with this assay (Supplementary file 1), and the specificity was assumed as 100%. The crude prevalence of antiS antibodies was 56.7% (95% CrI 53.6–59.8%) in November 2020 and 78.7% (95% CrI 75.6–81.4%) in April 2021. After correcting for sensitivity and reweighting by age and sex, the seroprevalence estimate was 60.0% (95% CrI 58.4–62.2%) in November 2020 and 83.3% (95% CrI 81.1–86.4%) in April 2021, compared to 68.0% (95% CrI 64.2–72.7%) and 99.5% (95% CrI 94.0–106.6%) estimated using our seroreversion correction model for November 2020 and March 2021. Note that the attack rate estimated by our model considers both infections and reinfections among seronegative individuals, hence, the confidence intervals higher than 100%. Of note, we measured the halflife of this assay using the serial repeat blood donors data available in Prete et al., 2022, obtaining a median halflife of 124.5 (interquartile range 74.7–258.0) days. In November, 6 months following the first wave in Manaus, some cases of seroreversion are expected to have occurred; as such, this remains an underestimate of the true cumulative attack rate by this point. Assuming no reinfections before November, the smaller seroprevalence measured with the antiS assay suggests that 8.0% of previously infected donors seroreverted before November 2020.
Derivation of the expression of the probability of a positive test
In this section, we derive the expression of the probability of a positive test $\theta [n,a]$ in terms of the agespecific weekly incidence $u[n,a]$. Let us denote the negation of an event $E$ as $\overline{E}$, and the probability of an event $E$ as $\mathbb{P}\left\{E\right\}$. To shorten the next equations, we also denote ${\mathcal{T}}^{+}\left(n,a\right)$ the event of a test applied to an individual from agesex group $a$ at week $n$ being positive, $I(n,a)$ the event of an individual from agesex group $a$ being infected at week $n$ such that the incidence at week $n$ and agesex group $a$ is $\mathbb{P}\left\{I\left(n,a\right)\right\}$, $I\left(1:n,a\right)={\bigcup}_{k=1}^{n}I(n,a)$ the event of an individual from group $a$ having being infected before week $n$ and $\mathcal{C}\left(a\right)$ the event of an infected individual from group $a$ seroconverting after infection. We consider that the initial sensitivity $\mathrm{s}{\mathrm{e}}_{0}$ (i.e. the sensitivity right after seroconversion) and specificity $\mathrm{s}\mathrm{p}$ of the assay do not depend on the agesex group or on time.
The probability $\theta \left[n,a\right]$ of a test applied to a person from agesex group $a$ being positive at week $n$ is
The first term can be decomposed as
The term $\mathbb{P}\left\{{\mathcal{T}}^{+}\left(n,a\right)\mid I\left(k,a\right)\right\}$ can be further decomposed into
Assuming that an infected individual that did not seroconvert cannot have a positive test at any instant, we have $\mathbb{P}\left\{{\mathcal{T}}^{+}\left(n,a\right)\mid I\left(k,a\right),\overline{\mathcal{C}}\left(a\right)\right\}=0$. We approximate $\mathbb{P}\left\{{\mathcal{T}}^{+}\left(n,a\right)\mid I\left(k,a\right)\right\}$ to ${p}^{+}[nk]$ (i.e. the probability of a test being positive $nk$ weeks after seroconversion), neglecting the delay between infection and seroconversion. Since the mean delay between infection and seroreversion is smaller than 8 days as explained above, and since crude seroprevalence data are discretized using weeks as time unit, this delay has small influence on seroprevalence estimates. Because $\mathbb{P}\left\{\mathcal{C}\left(a\right)\mid I\left(k,a\right)\right\}$ is the sensitivity $\mathrm{s}{\mathrm{e}}_{0}$ of the assay and $\mathbb{P}\left\{I\left(k,a\right)\right\}$ is the incidence $u[k,a]$, we have $\mathbb{P}\left\{{\mathcal{T}}^{+}\left(n,a\right),I\left(1:n,a\right)\right\}$ $=\mathrm{s}{\mathrm{e}}_{0}\sum _{k=1}^{n}{p}^{+}\left[nk\right]u\left[k,a\right]$.
The second term of $\theta [n,a]$ is
where $\text{sp}=\mathbb{P}\left\{{\mathcal{T}}^{+}\left(n,a\right)\mid \overline{I}\left(1:n,a\right)\right\}$ is the specificity of the assay, which does not change over time.
Therefore, a simpler expression for $\theta [n,a]$ is obtained:
Description of the method used to validate the seroprevalence and IFR for 2020
To validate the seroprevalence and IFRs estimated for 2020, we recalculate these quantities by measuring the prevalence in December 2020 with a smaller threshold equal to 0.1 to partially account for seroreversion and correct for sensitivity and specificity, without explicitly incorporating a method to correct for seroreversion (Appendix 1—figure 23).
Let $\mathrm{T}\mathrm{P},\mathrm{F}\mathrm{N},\mathrm{F}\mathrm{P}$, and $\mathrm{T}\mathrm{N}$ be, respectively, the number of true positives, false negatives, false positives and true negatives obtained from plasma donors and the prepandemic cohort in Manaus using a threshold 0.1. We use a uniform distribution in the interval [0, 1] as prior for the seroprevalence of agesex group $a$, and also for the sensitivity $\mathrm{s}\mathrm{e}$ and specificity $\mathrm{s}\mathrm{p}$. The posterior distribution of the sensitivity and specificity is, respectively, $\mathrm{B}\mathrm{e}\mathrm{t}\mathrm{a}\left(1+\mathrm{T}\mathrm{P},1+\mathrm{F}\mathrm{N}\right)$ and $\mathrm{B}\mathrm{e}\mathrm{t}\mathrm{a}\left(1+\mathrm{T}\mathrm{N},1+\mathrm{F}\mathrm{P}\right)$. The seroprevalence $\rho \left[a\right]$ of agesex group $a$ is distributed according to a binomial distribution of size $T\left[a\right]$ (the number of tests for this agesex group) and probability $\mathrm{s}\mathrm{e}\times \rho \left[a\right]+(1\mathrm{s}\mathrm{p})(1\rho \left[a\right])$. To draw a posterior sample of $\rho \left[a\right]$, we draw a posterior sample of $se$ and $sp$ and from the auxiliary variable $Z\left[a\right]\sim \mathrm{B}\mathrm{e}\mathrm{t}\mathrm{a}({T}^{+}\left[a\right]+1,T\left[a\right]{T}^{+}\left[a\right]+1)$, which represents the raw measured prevalence. Then, we compute the prevalence adjusted by sensitivity and specificity through $\rho \left[a\right]=\left(0,\frac{Z\left[a\right]+\text{sp}1}{\text{se}+\text{sp}1}\right)\text{}.$ Finally, a sample of the IFR is then drawn from $\mathrm{B}\mathrm{e}\mathrm{t}\mathrm{a}(1+D\left[a\right],1+\lfloor \mathrm{p}\mathrm{o}\mathrm{p}\left[a\right]\times \rho \left[a\right]\rfloor D[a\left]\right)$.
Selection of SARI hospitalisations and deaths to estimate the IFR and IHR
In the first months of the SARSCoV2 epidemic in Brazil, a small proportion of SARI cases were tested for SARSCoV2, leading to a large number of nonnotified deaths. For this reason, instead of using only COVID19 confirmed hospitalisations or deaths to estimate the IFR and IHR, we also included SARI hospitalisations or deaths with unknown aetiology. This approach was proposed in de Souza et al., 2020. In this section, we investigate the validity of this approach by comparing SARI hospitalisations and deaths in the eight cities recorded between 2013 and 2021.
Appendix 1—figure 25 shows the monthly number of SARI deaths from 2013 to 2021 disaggregated by case classification (confirmed SARSCoV2 infection, infection confirmedly caused by other respiratory viruses, and cases with unknown or missing aetiology). The monthly number of SARI deaths increased abruptly in March 2020 due to the SARSCoV2 epidemic to 3810, 14.5 times larger than the previous peak of SARI cases in April 2016. Despite that only 58.6% of the SARI deaths in March 2020 were confirmed as COVID19 cases, and 39.7% had unknown or missing aetiology, suggesting that most SARI deaths with unknown aetiology were nonnotified COVID19 deaths. Even if there was an epidemic of another respiratory virus in March 2020 that caused a number of cases similar to April 2016, it would only explain 17.4% of the SARI cases with unknown or missing aetiology in March 2020.
The proportion of each case classification among monthly SARI deaths is shown in Appendix 1—figure 4b. The proportion of deaths with unknown or missing aetiology had a peak in September 2020, decreasing over time in the following months likely due to the increasing availability of tests. Therefore, the effect of taking SARI into account is more important in the first year of the epidemic in Brazil.
Similar patterns are observed for SARI hospitalisations, as shown in Appendix 1—figure 26. However, SARI hospitalisations in March 2020 are only 4.7 times larger than the previous peak of monthly SARI hospitalisations in April 2016, suggesting that our approach is more sensitive to SARI cases caused by other respiratory viruses when hospitalisations are used. Nevertheless, an epidemic of other respiratory viruses similar to the historical peak of SARI cases in April 2016 would only explain 42% of the SARI cases with unknown or missing aetiology in March 2020.
Method used to estimate ${\mathit{p}}^{+}\left[\mathit{n}\right]$ from repeat blood donors
Here we summarise the stepbystep procedure used to estimate ${p}^{+}\left[n\right]$, the probability of an individual remaining seropositive $n$ weeks after seroconversion, described in Methods. The algorithm receives as inputs: The set of serial donations from ${N}_{\mathrm{d}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{s}}$ repeats blood donors who have at least one positive result and a second result with decaying S/C; the daily incidence over time for the repeat blood donors cohort ${u}_{\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{t}}\left[n\right]$ (see Methods); the number of samples ${N}_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{s}}$ used to estimate the probability distribution of the time to seroreversion. The output of the algorithm is an estimate of ${p}^{+}\left[n\right]$.
The algorithm is described below:
For $i\in 1,2,\cdots ,{N}_{\mathrm{d}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{s}}:$
Calculate the date of seroreversion for donor $i$ by computing the instant where the exponential curve that passes through the last positive donation and first negative donation after seroconversion (if seroreversion occurred) or the two last positive donations cross the threshold, as illustrated in Appendix 1—figure 10. Denote it by ${t}_{i}^{}.$
Denote ${t}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ as the last negative result of the donor before seroconversion or set ${t}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ as 1 March 2020, if the donor had no positive results before seroconversion. Denote ${t}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ as the date of the first positive result. The unobserved date of seroconversion belongs to the interval $[{t}_{\mathrm{m}\mathrm{i}\mathrm{n}},{t}_{\mathrm{m}\mathrm{a}\mathrm{x}}]$ and its probability mass function is given by
${p}_{i}\left[n\right]=\{\begin{array}{ll}\frac{{u}_{\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{t}}\left[n\right]}{\sum _{k={t}_{\mathrm{m}\mathrm{i}\mathrm{n}}}^{{t}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{u}_{\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{t}}\left[k\right]}& ,\text{}\text{}\text{}{t}_{\mathrm{m}\mathrm{i}\mathrm{n}}\le n\le {t}_{\mathrm{m}\mathrm{a}\mathrm{x}}\\ \phantom{\rule{2em}{0ex}}0& ,\text{}\text{}\text{}\text{otherwise}\end{array}.$Generate $N}_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{s}$ samples $\mathrm{\Delta}{t}_{i}^{\left(1\right)},\mathrm{\Delta}{t}_{i}^{\left(2\right)},\cdots ,\mathrm{\Delta}{t}_{i}^{\left({N}_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{s}}\right)}$ from $\mathrm{\Delta}{t}_{i}={t}_{i}^{}{t}_{i}^{+}$, where ${t}_{i}^{+}\sim {p}_{i}\left[n\right]$.
Calculate the empirical probability mass function of $\mathrm{\Delta}{t}_{i}$ by computing the empirical histogram of the generated samples $\mathrm{\Delta}{t}_{i}^{\left(1\right)},\mathrm{\Delta}{t}_{i}^{\left(2\right)},\cdots ,\mathrm{\Delta}{t}_{i}^{\left({N}_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{s}}\right)}$ and denote it as ${p}_{\mathrm{d}\mathrm{a}\mathrm{y}}^{}\left[n\right]$.
Convert ${p}_{\mathrm{d}\mathrm{a}\mathrm{y}}^{}\left[n\right]$ from days to weeks, obtaining ${p}_{\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{k}}^{}\left[n\right]$:
${p}_{\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{k}}^{}\left[n\right]=\frac{1}{7}\sum _{i=1}^{7}\sum _{j=7n+1}^{7\left(n+1\right)}{p}_{\mathrm{d}\mathrm{a}\mathrm{y}}^{}\left[ji\right].$Calculate the probability of an individual remaining seropositive $n$ weeks after seroconversion ${p}^{+}\left[n\right]$ as
${p}^{+}\left[n\right]=1\sum _{i=1}^{n}{p}_{\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{k}}^{}\left[k\right].$
Description of the Bayesian model used to estimate the seroprevalence
We now present an objective description of the seroreversion correction model introduced in Methods. This is a Bayesian model that produces age and sexspecific seroprevalence estimates corrected for seroreversion, sensitivity, and specificity. The model receives as inputs: The probability of seropositivity $n$ weeks after seroconversion ${p}^{+}\left[n\right]$; the weekly number of tests $T[n,a]$ and weekly number of positive tests ${T}^{+}\left[n,a\right]$ at week $n$ for agesex group $a$; the number of true positives ($\mathrm{T}\mathrm{P}$), true negatives ($\mathrm{T}\mathrm{N}$), false positives ($\mathrm{F}\mathrm{P}$) and false negatives ($\mathrm{F}\mathrm{N}$) used to determine the sensitivity and specificity of the assay; the maximum seroprevalence allowed $b$. In this work, we use $b=2$ to partially account for reinfections. The model generates as output posterior samples from the weekly incidence $u[n,a]$ for agesex group $a=\mathrm{1,2},\cdots ,M$ and week $n=\mathrm{1,2},\cdots ,N$. For this reason, the model generates posterior samples from the sensitivity $\mathrm{s}{\mathrm{e}}_{0},$ the specificity $\mathrm{s}\mathrm{p}$, the normalised incidence ${u}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}[n,a]$, and the final seroprevalence ${\rho}_{\mathrm{m}\mathrm{a}\mathrm{x}}\left[a\right]$, obtaining $u[n,a]$ from these parameters.
The Bayesian model is described below:
Prior distributions:
$\mathrm{s}{\mathrm{e}}_{0}\sim \mathrm{B}\mathrm{e}\mathrm{t}\mathrm{a}(1+\mathrm{T}\mathrm{P},1+\mathrm{F}\mathrm{N})$$\mathrm{s}\mathrm{p}\sim \mathrm{B}\mathrm{e}\mathrm{t}\mathrm{a}(1+\mathrm{T}\mathrm{N},1+\mathrm{F}\mathrm{P})$${u}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}\left[1:N,a\right]\sim \mathrm{D}\mathrm{i}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{h}\mathrm{l}\mathrm{e}\mathrm{t}\left(\mathrm{1,1},\cdots ,1\right)\forall a$${\rho}_{\mathrm{m}\mathrm{a}\mathrm{x}}\left[a\right]\sim \mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\left(0,b\right)\forall a$Auxiliary variables:
$u\left[n,a\right]={u}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}\left[n,a\right]\times {\rho}_{\mathrm{m}\mathrm{a}\mathrm{x}}\left[a\right],\forall n,a$$\theta \left[n,a\right]=\mathrm{s}{\mathrm{e}}_{0}\sum _{k=1}^{n}{p}^{+}\left[nk\right]u\left[k,a\right]+\left(1\mathrm{s}\mathrm{p}\right)\left(1\sum _{k=1}^{n}u\left[k,a\right]\right)\forall n,a$Likelihood:
${T}^{+}\left[n,a\right]\sim \mathrm{B}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{a}\mathrm{l}\left(T\left[n,a\right],\theta \left[n,a\right]\right)\forall n,a$
We note the estimated seroprevalence is the cumulative sum of the obtained incidence $u[n,a]$ and can therefore be larger than 1 due to reinfections. Also, since this model assumes all infections occur in seronegative donors, $u[n,a]$ can be interpreted as the incidence in seronegative donors, and reinfections among seropositive individuals are not detected.
Summary of the method used to estimate the lower bound for the attack rate of the Gamma VOC in Manaus and the upper bound for the IFR
We now present a summary of the procedure used to infer bounds for the agespecific attack rate and IFR of the Gammadominated wave in Manaus explained in Methods. This procedure was also used to estimate the IHR, but in this case, the number of hospitalisations was used instead of the number of deaths.
The algorithm is executed independently for each age group and receives as inputs: The number of deaths $D$ with symptom onset between 16 December 2020 and 15 March 2021; the monthly number of positive tests ${T}^{+}\left[n\right]$ and the monthly number of tests $T\left[n\right]$ for $n\in \left\{\mathrm{12,13,14,15}\right\}$ , i.e., from December 2020 ($n=12)$ to March 2021 ($n=15$); the number of true positives ($\mathrm{T}\mathrm{P}$) and false negatives ($\mathrm{F}\mathrm{N}$) from the convalescent plasma donors cohort; population size $\mathrm{p}\mathrm{o}\mathrm{p}$.
The algorithm produces as outputs posterior samples of the maximum attack rate for the Gamma wave in Manaus (${\mathrm{A}\mathrm{R}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$) and the minimum IFR ($\mathrm{I}\mathrm{F}{\mathrm{R}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$) but also generates posterior samples from the following auxiliary variables: The incidence between months $n$ and $n+1$ denoted as $u\left[n\right]$, and the seroprevalence in December 2020 (month $n=12$) denoted as ${\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}}$ .
First, we generate posterior samples from ${\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}}$ and $u\left[n\right]$ using the Bayesian model described below:
Prior distributions:
${\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}}\sim \mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\left(\mathrm{0,1}\right)$$\left({u}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}\left[12\right],{u}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}\left[13\right],{u}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}\left[14\right]\right)\sim \mathrm{D}\mathrm{i}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{h}\mathrm{l}\mathrm{e}\mathrm{t}(\mathrm{1,1},1)$${u}_{\mathrm{m}\mathrm{a}\mathrm{x}}\sim \mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\left(\mathrm{0,1}\right)$Auxiliary variables:
$u\left[n\right]={u}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}\left[n\right]\times {u}_{\mathrm{m}\mathrm{a}\mathrm{x}}\left[a\right],n\in \left\{\mathrm{12,13,14}\right\}$Likelihood:
${T}^{+}\left[n,a\right]\sim \mathrm{B}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{a}\mathrm{l}\left(T\left[n\right],{\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}}+\sum _{k=12}^{n1}u\left[k\right]\right),n\in \left\{\mathrm{12,13,14,15}\right\}$
Then, for each posterior sample generated by the Bayesian model:
Draw a sample from $\mathrm{s}\mathrm{e}\sim \mathrm{B}\mathrm{e}\mathrm{t}\mathrm{a}(1+\mathrm{T}\mathrm{P},1+\mathrm{F}\mathrm{N})$.
Compute the incidence corrected by sensitivity ${u}^{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}\left[n\right]=\frac{u\left[n\right]}{\mathrm{s}\mathrm{e}}$ .
Compute $\hat{\mathrm{A}\mathrm{R}}=\sum _{n=12}^{14}{u}^{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}\left[n\right].$
Compute $\mathrm{A}{\mathrm{R}}_{\mathrm{m}\mathrm{a}\mathrm{x}}={\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}}+\hat{\mathrm{A}\mathrm{R}}$ .
Draw a sample from the lower bound of the IFR as
$\mathrm{I}\mathrm{F}{\mathrm{R}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\sim \mathrm{B}\mathrm{e}\mathrm{t}\mathrm{a}\left(1+D,1+\u230a\mathrm{A}{\mathrm{R}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\times \mathrm{p}\mathrm{o}\mathrm{p}\u230bD\right).$
Data availability
All serological data required to reproduce the analyses are available at Data Dryad (doi:https://doi.org/10.5061/dryad.dz08kps08) and can be downloaded at https://datadryad.org/stash/dataset/doi:10.5061/dryad.dz08kps08. The codes used for the main analyses are available at https://github.com/CADDECENTRE/seroprevalence_eight_cities, (copy archived at swh:1:rev:67518ad26368c1f4856fdfd4c08673abeded4901).

Dryad Digital RepositoryData from: SARSCoV2 antibody dynamics in blood donors and COVID19 epidemiology in eight Brazilian state capitals.https://doi.org/10.5061/dryad.dz08kps08
References

SoftwareReport 34: COVID19 infection fatality ratio: estimates from seroprevalenceReport 34.

Epidemiological and clinical characteristics of the COVID19 epidemic in BrazilNature Human Behaviour 4:856–865.https://doi.org/10.1038/s4156202009284

Second wave of COVID19 in Brazil: younger at higher riskEuropean Journal of Epidemiology 36:441–443.https://doi.org/10.1007/s10654021007508

SARScov2 antibody prevalence in Brazil: results from two successive nationwide serological household surveysThe Lancet. Global Health 8:e1390–e1398.https://doi.org/10.1016/S2214109X(20)303879

The duration, dynamics and determinants of SARScov2 antibody responses in individual healthcare workersClinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America 73:e699–e709.https://doi.org/10.1093/cid/ciab004

Comparison of SARScov2 IgM and IgG seroconversion profiles among hospitalized patients in two us citiesDiagnostic Microbiology and Infectious Disease 99:115300.https://doi.org/10.1016/j.diagmicrobio.2020.115300

Reinfection by the SARScov2 gamma variant in blood donors in manaus, BrazilBMC Infectious Diseases 22:127.https://doi.org/10.1186/s1287902207094y

Are seroprevalence estimates for severe acute respiratory syndrome coronavirus 2 biased?The Journal of Infectious Diseases 222:1772–1775.https://doi.org/10.1093/infdis/jiaa523
Decision letter

James M McCawReviewing Editor; The University of Melbourne, Australia

Miles P DavenportSenior Editor; University of New South Wales, Australia

Ivo MuellerReviewer; Walter and Eliza Hall Institute of Medical Research, Australia
In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.
Decision letter after peer review:
Thank you for submitting your article "SARSCoV2 antibody dynamics in blood donors and COVID19 epidemiology in eight Brazilian state capitals: A serial crosssectional study" for consideration by eLife. Your article has been reviewed by 2 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Miles Davenport as the Senior Editor. The following individual involved in the review of your submission has agreed to reveal their identity: Ivo Mueller (Reviewer #1).
The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.
In preparing a revised manuscript, please consider and address all comments raised by the reviewers. I draw your attention to one issue in particular though:
– The methodology uses deaths up to 15 Dec 2020 and compares that to the cumulative infections on 16 Dec 2020. As deaths lag infections, this will introduce a bias in the estimates of the IFR. While the bias is likely small due to the long study period and timing of waves of infection, in general, the approach should be adjusted to account for that lag.Reviewer #1 (Recommendations for the authors):
The authors conducted a retrospective serosurveillance study of blood donor samples from the 8 largest cities in Brazil to determine the heterogeneity of age and sexspecific exposure to SARSCoV2 infections and the resulting infection hospitalisation (IHR) and fatality rates (IFR). For Manaus, the observation period fully covered both primary and the Γ variantofconcern wave allowing the investigators to compare IFRs between the two wave/viral variants.
The use of serology to track the COVID pandemic is complicated by the relatively rapidly waning antibody responses that lead to infected individuals' seroreverting within 36 months after exposure. To adjust for that the authors developed an improved Bayesian seroreversion correction model that draws posterior samples from the incidence over time corrected by sensitivity, specificity, and seroreversion rates drawn from repeat blood donor samples. This allowed them to not only undertake a robust and detailed investigation of SARSCoV2 exposure patterns in Brazil and highlight the difference in the epidemic in different cities in Brazil but also to develop a methodology that can be applied for serosurveillance of other pathogens.
This is a welldesigned and executed study and very impressive in its scope and detail.
While the methods used for the seroreversion estimation are not entirely novel but an extension of the approaches previously developed by Buss et al. 2021, their adjustments/addition are substantial and by deriving distribution from repeat blood donors and estimating serologyprevalence for each age group separately, their results will be more robust and accurate at least for infections acquired in the first wave.
As the authors outline very transparently, the estimations of attack/exposure rates in the 2nd/γ wave in Manaus are more difficult as their method does not allow identifying reinfection in already seropositive individuals. Their method and assumption for estimating lower bounds for IFR and IHR for γ seem reasonable given the large difference in estimate IFR between Γ and 1st wave. This shortcoming may however become more pertinent if the same methods were used to calculate IFRs also for subsequent δ or omicron waves. While the authors do state the lower reliability of the inferences of attack rates towards the end of the time series, some more reflection on the circumstance/pandemic time frames that this approach can reliably be applied to might be useful.
Similarly, while blood donors are an easy source of blood samples they are a biased convenience sample of the overall population that the death and hospitalisations are drawn from. The authors show such biased for age, but other variables such as gender, socioeconomic status, or general health status (and thus underlying health condition) may introduce further biases. While these may not change the overall time patterns of epidemic size, they might explain some of the smaller differences between cities or reasons. The authors are therefore very correct in stating that studies comparing blood donors with the general population are essential if blood donor surveillance is to become a standard tool for epidemic monitoring.
The heterogeneous patterns in attack rates are important for a more indepth understanding of the pandemic course during a time and in locations where case ascertainment was low thus data on infection prevalence from diagnostic testing is very poor and difficult to interpret. Overall, they seem quite well in line with what was observed in other countries where overall case ascertainment was higher.
Despite its limitations, this is a very impressive and wellexecuted study that sets a high standard for other studies of serosurveillance using blood donors.Reviewer #2 (Recommendations for the authors):
In the proposed paper, the authors use the results of antibody testing in samples from blood donations in different places in Brazil during the first year of the SARSCoV2 pandemic (2020). They develop models to account for antibody waning in estimating the cumulative seropositivity. They then use reported death data to infer the underlying IFR. This is a very large study, with an impressive amount of data. Understanding underlying differences in IFR across communities and the potential difference in IFR by variant remains of interest.
To estimate IFR, the authors count the number of deaths occurring prior to December 15, 2020, they then compare this to the proportion infected at December 16. This will lead to an underestimation, as the time from infection to death can be weeks – many individuals infected in midDecember 2020 who went on to die would not be included in the numerator. The authors could either use a later cutoff for the deaths or use deconvolution to estimate the total deaths attributable to seroprevalence at the cutoff date.
Furthermore, it would be useful to understand the potential for misclassification of deaths, as this is critical to the IFR estimates. The authors use SARI deaths rather than COVID19specific deaths. It would be good to understand what proportion of the SARI deaths were ultimately attributed to COVID19 and how that changed over time. Maybe the authors could use the SARI deaths from the previous year as a reference for underlying nonCOVID19 SARI?
Line 285. I was confused as to why a higher threshold limits the maximum number of reinfections? Is this as it would imply a higher antibody load and therefore a lower risk of reinfection.
Line 351. Is the 203 a 'mean' time between seroconversion and seroreversion? Also, what are the units – days?
Two important age groups are not included in the blood bank data – those under 16y and those >64y. It was unclear to me how they were included in the overall IFR estimates (Figure 4).
Table 1. It was unclear to me what the differences between columns 2 and 3 are. Should column 3 maybe be titled 'Attack rate'?
In Figure 2 – the model results that adjust for seroreversion are lower than the crude estimates in pretty much each location for part of the study period. I would imagine that adjusting for seroreversion could only increase the seroprevalence.
Many of the paragraphs in the Results section are repetitions of the methods and could be removed. This will improve the readability of the paper.
Line 282 – what is S/C?
https://doi.org/10.7554/eLife.78233.sa1Author response
Reviewer #1 (Recommendations for the authors):
The authors conducted a retrospective serosurveillance study of blood donor samples from the 8 largest cities in Brazil to determine the heterogeneity of age and sexspecific exposure to SARSCoV2 infections and the resulting infection hospitalisation (IHR) and fatality rates (IFR). For Manaus, the observation period fully covered both primary and the Γ variantofconcern wave allowing the investigators to compare IFRs between the two wave/viral variants.
The use of serology to track the COVID pandemic is complicated by the relatively rapidly waning antibody responses that lead to infected individuals' seroreverting within 36 months after exposure. To adjust for that the authors developed an improved Bayesian seroreversion correction model that draws posterior samples from the incidence over time corrected by sensitivity, specificity, and seroreversion rates drawn from repeat blood donor samples. This allowed them to not only undertake a robust and detailed investigation of SARSCoV2 exposure patterns in Brazil and highlight the difference in the epidemic in different cities in Brazil but also to develop a methodology that can be applied for serosurveillance of other pathogens.
We thank the reviewer for the kind remarks.
This is a welldesigned and executed study and very impressive in its scope and detail.
While the methods used for the seroreversion estimation are not entirely novel but an extension of the approaches previously developed by Buss et al. 2021, their adjustments/addition are substantial and by deriving distribution from repeat blood donors and estimating serologyprevalence for each age group separately, their results will be more robust and accurate at least for infections acquired in the first wave.
As the authors outline very transparently, the estimations of attack/exposure rates in the 2nd/γ wave in Manaus are more difficult as their method does not allow identifying reinfection in already seropositive individuals. Their method and assumption for estimating lower bounds for IFR and IHR for γ seem reasonable given the large difference in estimate IFR between Γ and 1st wave. This shortcoming may however become more pertinent if the same methods were used to calculate IFRs also for subsequent δ or omicron waves. While the authors do state the lower reliability of the inferences of attack rates towards the end of the time series, some more reflection on the circumstance/pandemic time frames that this approach can reliably be applied to might be useful.
Similarly, while blood donors are an easy source of blood samples they are a biased convenience sample of the overall population that the death and hospitalisations are drawn from. The authors show such biased for age, but other variables such as gender, socioeconomic status, or general health status (and thus underlying health condition) may introduce further biases. While these may not change the overall time patterns of epidemic size, they might explain some of the smaller differences between cities or reasons. The authors are therefore very correct in stating that studies comparing blood donors with the general population are essential if blood donor surveillance is to become a standard tool for epidemic monitoring.
The heterogeneous patterns in attack rates are important for a more indepth understanding of the pandemic course during a time and in locations where case ascertainment was low thus data on infection prevalence from diagnostic testing is very poor and difficult to interpret. Overall, they seem quite well in line with what was observed in other countries where overall case ascertainment was higher.
Despite its limitations, this is a very impressive and wellexecuted study that sets a high standard for other studies of serosurveillance using blood donors.
We appreciate your suggestions. Our method can be applied to Δ and Omicron waves as long as the initial crude seroprevalence is small. In addition, it cannot distinguish seroconversion due to vaccination or natural infection. As such, it is more interesting to use our approach in regions or timeperiods where vaccines that induce antinucleocapsid antibodies were not frequently administered. We added the sentence below in line 350 to discuss the reliability of our approach to estimate the attack rate of epidemics with nonnegligible rates of reinfection.
“This method can be applied to estimate upper bounds for the attack rate of epidemics driven by other lineages with high rates of reinfection such as Delta and Omicron VOCs, but as previously highlighted the upper bound is only informative if the initial crude seroprevalence is small. This may not be the case in regions where vaccines inducing antinucleocapsid antibodies were applied, as it is not possible to distinguish vaccination from natural infection based only on antiN serological data.”
We also added a sentence in line 285 to emphasize the increasing uncertainty of the seroprevalence and IFR estimates over time:
“We note that the proposed seroreversion correction model can be used to estimate the attack rate and IFR of epidemics driven by other lineages in other regions. However, the uncertainty of the seroprevalence estimate increases over time, as a larger amount of seroreversion needs to be corrected. Therefore, estimated attack rates and IFRs suffer from larger uncertainty when longer time periods are considered.”
Reviewer #2 (Recommendations for the authors):
In the proposed paper, the authors use the results of antibody testing in samples from blood donations in different places in Brazil during the first year of the SARSCoV2 pandemic (2020). They develop models to account for antibody waning in estimating the cumulative seropositivity. They then use reported death data to infer the underlying IFR. This is a very large study, with an impressive amount of data. Understanding underlying differences in IFR across communities and the potential difference in IFR by variant remains of interest.
To estimate IFR, the authors count the number of deaths occurring prior to December 15, 2020, they then compare this to the proportion infected at December 16. This will lead to an underestimation, as the time from infection to death can be weeks – many individuals infected in midDecember 2020 who went on to die would not be included in the numerator. The authors could either use a later cutoff for the deaths or use deconvolution to estimate the total deaths attributable to seroprevalence at the cutoff date.
Furthermore, it would be useful to understand the potential for misclassification of deaths, as this is critical to the IFR estimates. The authors use SARI deaths rather than COVID19specific deaths. It would be good to understand what proportion of the SARI deaths were ultimately attributed to COVID19 and how that changed over time. Maybe the authors could use the SARI deaths from the previous year as a reference for underlying nonCOVID19 SARI?
The SIVEPGripe dataset contains not only the date of death for each deceased patient, but also the date of first symptoms. As such, to estimate the IFR for 2020 we use deaths from patients with symptom onset before December 15, instead of using deaths that occurred before December 15. For this reason, it is not necessary to take into account the delay between deaths and symptoms onset. We apologize that this information is not clear in the manuscript.
This information was mentioned in line 263:
“To estimate the IFR in 2020, we use the seroprevalence estimated by our model for December 16, 2020 and select only SARI deaths with symptoms onset between March 1st and December 15, 2020.”
To clarify this sentence, we added a second sentence after it:
“Selecting deaths based on the date of first symptoms instead of date of death was possible because SIVEPGripe contains the date of symptom onset for each individual.”
We also emphasized we used the date of symptom onset in the legend of Figure 4:
“The number of deaths was obtained from the SIVEPGripe reporting system including all SARI deaths with symptom onset between March 1^{st}, 2020 and December 15^{th}, 2021.”
We appreciate your suggestion to analyze the potential impact of misclassification of deaths. We included a reference in line 261 for the first paper that uses SARI deaths as a proxy for COVID19 deaths. We also added a supplementary analysis in Appendix 1 (line 960), showing that it is reasonable to assume the large majority of unspecified SARI deaths after March 2020 are undetected COVID19 deaths. Furthermore, as explained in the new supplementary analysis, the proportion of SARI deaths with unknown etiology decays with time as tests become more available. Therefore, the monthly number of imputed COVID19 deaths based on unspecified SARI deaths decreases with time, thus the effect of imputation in the IFR estimate is more relevant during the first months of the epidemic.
Line 285. I was confused as to why a higher threshold limits the maximum number of reinfections? Is this as it would imply a higher antibody load and therefore a lower risk of reinfection.
Using a higher threshold lowers the number of seropositive donors in December 2020, limiting the number of estimated reinfections among seropositive donors and leading to a smaller estimate of the upper bound for the attack rate.
We believe the sentence in Line 285 of the original manuscript is not clear enough. Therefore, we rewrote this sentence, and added two paragraphs in Lines 314 and 336 of the revised version of the manuscript to improve the explanation of our method. We hope this modification clarifies the reason why we use a larger threshold of 1.4 to estimate the attack rate of the second wave in Manaus. We also improved the description of our method in Appendix 1 – Algorithm 3 (moved to the main text in Appendix 1).
“We first estimate the attack rate of the second wave using a Bayesian model that does not take reinfections into account. This model also neglects seroreversion for individuals infected during the second wave due to the small interval of three months considered in this analysis (see Appendix 1 for a complete description of the model). Denoting as $\hat{\text{AR}}$ the attack rate estimated by this model, the true attack rate $\mathrm{A}\mathrm{R}$ is given by $\text{AR}=\hat{\text{AR}}+R+S$, where $R$ is the proportion of donors that were seropositive in December 2020 and subsequently had a reinfection, and $S$ is the proportion of donors that were seropositive in December 2020 and became seronegative in the following months. Since $R+S$ cannot be greater than the seroprevalence in December 2020 (denoted as $\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}$), the upper bound for the attack rate is $\text{AR}}_{max}=\hat{\text{AR}}+{\rho}_{\text{December}$. Therefore, the upper bound is obtained assuming that all individuals that were seropositive in December were later reinfected or were seronegative in March 2021.
To estimate $\text{AR}}_{max$, we compute the monthly number of positive tests ${T}^{+}\left[n\right]$ from December 2020 to March 2021 for each agesex group, as well as the number of True Positive (TP) and False Negatives (FN) from convalescent plasma donors and the number of False Positives (FP) and True Negatives (TN) from the prepandemic blood donors cohort in Manaus (Supplementary File 1). The Bayesian model generates posterior samples of the crude monthly incidence and the crude seroprevalence in December $\rho}_{\mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}$. We then correct the crude incidence by the sensitivity of the assay to obtain posterior samples of $\hat{\mathrm{A}\mathrm{R}}$, which are then added to the posterior samples of ${\rho}_{\mathrm{\text{December}}}$, resulting in samples of $\text{AR}}_{\text{max}$. As explained above, the lower bound for the IFR is then calculated using the upper bound of the attack rate and the number of deaths with symptom onset between December 16 and March 15. This procedure is repeated for each agesex group independently, and is summarised in Appendix 1.
Only small estimates of the upper bound for the attack rate are informative, as in scenarios where $\rho}_{\text{December}$ is small. To limit $\rho}_{\text{December}$, we estimate the incidence using a threshold of 1.4 signaltocutoff (the upper threshold recommended by the manufacturer) instead of 0.49 signaltocutoff (the lower threshold recommended by the manufacturer), and correct for sensitivity based on 163 true positives and 30 false negatives in the plasma donors cohort. Since the specificity of the test using a threshold of 1.4 is 99.9%, and since it is not straightforward to take the specificity into account when reinfections are allowed, we do not correct for specificity in this analysis.”
Line 351. Is the 203 a 'mean' time between seroconversion and seroreversion? Also, what are the units – days?
203 and 280 are respectively the median time between seroconversion and seroreversion for repeat blood donors and convalescent plasma donors, measured in days. We changed the sentence to:
“yielding a shorter median time between seroconversion and seroreversion (203 [147 – 294] days versus 280 [175 – 441] days)”.
Two important age groups are not included in the blood bank data – those under 16y and those >64y. It was unclear to me how they were included in the overall IFR estimates (Figure 4).
To facilitate the comparison of the IFRs across cities, we combined the agespecific IFR estimates to obtain an overall IFR for individuals aged between 16 and 64 instead of an overall IFR that includes all age groups. As such, the IFR of individuals older than 64 or younger than 16 is not included in this estimate. We highlighted in the legend of Figure 4 that overall IFR estimates consider only the age range 1664, and added a paragraph in line 279 to clarify this information:
“To infer the IFR, we considered the age groups 1624, 2534, 3544, 45,54 and 5564. We applied the same method to estimate the overall IFR but using a single age group containing all individuals aged between 16 and 64. Therefore, IFR of individuals older than 64 or younger than 16 are not included in the overall IFR estimates. The method used to infer the IFR was also applied to compute the InfectionHospitalisation Rate (IHR), but we used the number of hospitalisations with SARI instead of the number of deaths.”
Table 1. It was unclear to me what the differences between columns 2 and 3 are. Should column 3 maybe be titled 'Attack rate'?
Column 3 is the estimated attack rate, obtaining by correcting the crude seroprevalence by sensitivity, specificity, seroreversion and reweighting by age and sex. Column 2 is the seroprevalence corrected by sensitivity, specificity and reweighted by age and sex, but not corrected for seroreversion.
We agree that ‘Attack Rate’ is a better name for the 3rd column. We also changed the name of the 2nd column to “Adjusted seroprevalence with no correction for seroreversion (%)” to clarify its meaning.
In Figure 2 – the model results that adjust for seroreversion are lower than the crude estimates in pretty much each location for part of the study period. I would imagine that adjusting for seroreversion could only increase the seroprevalence.
Figure 2 shows the adjusted seroprevalence obtained by aggregating all age and sex groups, but the model produces age and sex specific seroprevalence estimates. Appendix 1 – Figure 16 compares the age and sex specific crude seroprevalence with the estimates from our model. In almost all locations, months and agesex groups, the estimated seroprevalence lie within or above the 95% confidence intervals of the crude seroprevalence.
However, in some cases the age and sex specific seroprevalence corrected for seroreversion is smaller than the crude seroprevalence. This would not be possible in deterministic models that fit exactly the measured seroprevalence such as in Buss et al., but it may happen in Bayesian models in time points where the crude seroprevalence does not agree with the model. Therefore, our Bayesian model not only corrects for seroreversion, but also partially removes inconsistent samples. This is because seroprevalence curves that cannot be reconstructed by the model generate a smaller likelihood, hence a smaller probability of being included in the set of samples generated by the model.
An inconsistent sample may occur in weeks where blood donors are not representative of the population, being biased towards seropositive or seronegative individuals, or due to sampling noise. This effect is discussed for Fortaleza in Line 466:
“The estimated seroprevalence in June and July in Fortaleza was significantly smaller than the measured seroprevalence without correction for seroreversion, even though the seroprevalence estimates disaggregated by age and sex (Appendix 1 – Figure 16) lie within or above the confidence intervals of the measured seroprevalence. This effect happened especially in women, which had a crude seroprevalence that was significantly larger than in men in June and July 2020, but became similar in the following months. It is possible that the seroreversion rate observed in Fortaleza had been faster than the rate estimated from repeat blood donors, in which case we undercorrected for seroreversion, underestimating the attack rate. However, a more likely explanation is that samples between March and July 2020 for Fortaleza are less representative of the population, since only 39.4% from 4,970 selected samples could have been retrieved and tested, compared to 97.0% for the other cities and months. As such, seropositive individuals from Fortaleza may have been more likely to donate in these months, leading to an overestimated crude seroprevalence.”
To better explain this effect, we added a paragraph in line 236:
“It is worth noting that the agespecific crude seroprevalence can be larger than the seroprevalence corrected for seroreversion in some weeks, as the model may remove outlier samples. This is because seroprevalence curves that cannot be reconstructed by the model (for example, due to bias or sampling noise) generate a small likelihood, hence a smaller probability of being included in the set of posterior samples generated by the model. Therefore, the model excludes weeks where donors are significantly biased towards more seropositive or more seronegative individuals.”
Many of the paragraphs in the Results section are repetitions of the methods and could be removed. This will improve the readability of the paper.
We appreciate your suggestion. We moved some of the paragraphs in the Results section to Methods and removed sentences that contained repeated information.
Line 282 – what is S/C?
S/C is an abbreviation for signaltocutoff, which is the analog result of the test. If the signaltocutoff is greater than or equal to the predefined threshold, the test result is positive. We added a sentence in line 89 to clarify the meaning of the abbreviation S/C:
“A test is considered positive if the obtained signaltocutoff (S/C) is greater or equal to a predefined threshold of 0.49.”
https://doi.org/10.7554/eLife.78233.sa2Article and author information
Author details
Funding
Itau Unibanco (Todos pela Saúde)
 Nuno R Faria
 Ester C Sabino
FAPESP (18/143890)
 Nuno R Faria
 Ester C Sabino
Medical Research Council (MR/S0195/1)
 Nuno R Faria
 Ester C Sabino
Wellcome Trust and Royal Society (Sir Henry Dale Fellowship 204311/Z/16/Z)
 Nuno R Faria
Gates Foundation (INV 034540 and INV034652)
 Nuno R Faria
 Ester C Sabino
National Heart, Lung, and Blood Institute (Recipient Epidemiology and Donor Evaluation Study HHSN268201100007I)
 Nuno R Faria
 Ester C Sabino
FAPESP (2019/218580)
 Carlos A Prete Jr
Fundacao Faculdade de Medicina
 Carlos A Prete Jr
CAPES (Finance Code 001)
 Carlos A Prete Jr
CNPq (304714/20186)
 Vítor H Nascimento
FAPESP
 Suzete C Ferreira
Programa Inova FIOCRUZCE/Funcap (Edital 01/2020 Number: FIO016700065.01.00/20 SPU Nº 06531047/2020)
 Fabio Miyajima
CNPq
 Manoel BarralNetto
JBS  Fazer o bem faz bem
 Rafael FO Franca
Medical Research Council (MR/V038109/1)
 Oliver Ratmann
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication. For the purpose of Open Access, the authors have applied a CC BY public copyright license to any Author Accepted Manuscript version arising from this submission.
Acknowledgements
This work was supported by the Itaú Unibanco 'Todos pela Saude' program and by CADDE/FAPESP (MR/S0195/1 and FAPESP 18/14389–0) (http://caddecentre.org/); Wellcome Trust and Royal Society Sir Henry Dale Fellowship 204311/Z/16/Z (NRF); the Gates Foundation (INV 034540 and INV034652) the National Heart, Lung, and Blood Institute Recipient Epidemiology and Donor Evaluation Study (REDS, now in its fourth phase, REDSIVP) for providing the blood donor demographic and zip code data for analysis (grant HHSN268201100007I); and the UK Medical Research Council under a concordat with the UK Department for International Development and Community Jameel and the NIHR Health Protection Research Unit in Modelling Methodology. CAPJ was supported by FAPESP (2019/218580) and Fundação Faculdade de Medicina. CAPJ, VHN were supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. VHN was supported by CNPq (304714/2018–6). SCF is supported by FAPESP. FM is supported by PROGRAMA INOVA FIOCRUZCE/Funcap, Edital 01/2020 Number: FIO0167–00065.01.00/20 SPU N° 06531047/2020. MBN is supported by CPNq. RFOF is supported by JBS  Fazer o bem faz bem. OR is supported by Medical Research Council MR/V038109/1.
The Blood Center SARSCoV2 Prevalence group is also composed by Cláudia M M Abrahim, Martirene A Silva, Fabíola S A Hanna, Adriana S N Ramos, Juqueline R Cristal and Samara Alves. We also thank Robert Verity for his critical review of the paper and suggestions.
Ethics
This project was approved by the Brazilian national research ethics committee, CONEP CAAE  30178220.3.1001.0068. The Brazilian national research committee (CONEP) waived for informed consent. All methods were performed in accordance with relevant guidelines and regulations.
Senior Editor
 Miles P Davenport, University of New South Wales, Australia
Reviewing Editor
 James M McCaw, The University of Melbourne, Australia
Reviewer
 Ivo Mueller, Walter and Eliza Hall Institute of Medical Research, Australia
Publication history
 Preprint posted: February 22, 2022 (view preprint)
 Received: February 28, 2022
 Accepted: September 17, 2022
 Accepted Manuscript published: September 22, 2022 (version 1)
 Accepted Manuscript updated: September 23, 2022 (version 2)
 Version of Record published: October 7, 2022 (version 3)
Copyright
© 2022, Prete, Buss, Whittaker et al.
This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.
Metrics

 973
 Page views

 216
 Downloads

 2
 Citations
Article citation count generated by polling the highest count across the following sources: PubMed Central, Crossref, Scopus.
Download links
Downloads (link to download the article as PDF)
Open citations (links to open the citations from this article in various online reference manager services)
Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)
Further reading

 Epidemiology and Global Health
Background:
Shortterm forecasts of infectious disease burden can contribute to situational awareness and aid capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise the predictive performance of such forecasts if multiple models are combined into an ensemble. Here, we report on the performance of ensembles in predicting COVID19 cases and deaths across Europe between 08 March 2021 and 07 March 2022.
Methods:
We used opensource tools to develop a public European COVID19 Forecast Hub. We invited groups globally to contribute weekly forecasts for COVID19 cases and deaths reported by a standardised source for 32 countries over the next 1–4 weeks. Teams submitted forecasts from March 2021 using standardised quantiles of the predictive distribution. Each week we created an ensemble forecast, where each predictive quantile was calculated as the equallyweighted average (initially the mean and then from 26th July the median) of all individual models’ predictive quantiles. We measured the performance of each model using the relative Weighted Interval Score (WIS), comparing models’ forecast accuracy relative to all other models. We retrospectively explored alternative methods for ensemble forecasts, including weighted averages based on models’ past predictive performance.
Results:
Over 52 weeks, we collected forecasts from 48 unique models. We evaluated 29 models’ forecast scores in comparison to the ensemble model. We found a weekly ensemble had a consistently strong performance across countries over time. Across all horizons and locations, the ensemble performed better on relative WIS than 83% of participating models’ forecasts of incident cases (with a total N=886 predictions from 23 unique models), and 91% of participating models’ forecasts of deaths (N=763 predictions from 20 models). Across a 1–4 week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over 4 weeks for incident death forecasts. In every forecast across 32 countries, the ensemble outperformed most contributing models when forecasting either cases or deaths, frequently outperforming all of its individual component models. Among several choices of ensemble methods we found that the most influential and best choice was to use a median average of models instead of using the mean, regardless of methods of weighting component forecast models.
Conclusions:
Our results support the use of combining forecasts from individual models into an ensemble in order to improve predictive performance across epidemiological targets and populations during infectious disease epidemics. Our findings further suggest that median ensemble methods yield better predictive performance more than ones based on means. Our findings also highlight that forecast consumers should place more weight on incident death forecasts than incident case forecasts at forecast horizons greater than 2 weeks.
Funding:
AA, BH, BL, LWa, MMa, PP, SV funded by National Institutes of Health (NIH) Grant 1R01GM109718, NSF BIG DATA Grant IIS1633028, NSF Grant No.: OAC1916805, NSF Expeditions in Computing Grant CCF1918656, CCF1917819, NSF RAPID CNS2028004, NSF RAPID OAC2027541, US Centers for Disease Control and Prevention 75D30119C05935, a grant from Google, University of Virginia Strategic Investment Fund award number SIF160, Defense Threat Reduction Agency (DTRA) under Contract No. HDTRA119D0007, and respectively Virginia Dept of Health Grant VDH215010141, VDH215010143, VDH215010147, VDH215010145, VDH215010146, VDH215010142, VDH215010148. AF, AMa, GL funded by SMIGE  Modelli statistici inferenziali per governare l'epidemia, FISR 2020Covid19 I Fase, FISR2020IP00156, Codice Progetto: PRJ0695. AM, BK, FD, FR, JK, JN, JZ, KN, MG, MR, MS, RB funded by Ministry of Science and Higher Education of Poland with grant 28/WFSN/2021 to the University of Warsaw. BRe, CPe, JLAz funded by Ministerio de Sanidad/ISCIII. BT, PG funded by PERISCOPE European H2020 project, contract number 101016233. CP, DL, EA, MC, SA funded by European Commission  DirectorateGeneral for Communications Networks, Content and Technology through the contract LC01485746, and Ministerio de Ciencia, Innovacion y Universidades and FEDER, with the project PGC2018095456BI00. DE., MGu funded by Spanish Ministry of Health / REACTUE (FEDER). DO, GF, IMi, LC funded by Laboratory Directed Research and Development program of Los Alamos National Laboratory (LANL) under project number 20200700ER. DS, ELR, GG, NGR, NW, YW funded by National Institutes of General Medical Sciences (R35GM119582; the content is solely the responsibility of the authors and does not necessarily represent the official views of NIGMS or the National Institutes of Health). FB, FP funded by InPresa, Lombardy Region, Italy. HG, KS funded by European Centre for Disease Prevention and Control. IV funded by Agencia de Qualitat i Avaluacio Sanitaries de Catalunya (AQuAS) through contract 2021021OE. JDe, SMo, VP funded by Netzwerk Universitatsmedizin (NUM) project egePan (01KX2021). JPB, SH, TH funded by Federal Ministry of Education and Research (BMBF; grant 05M18SIA). KH, MSc, YKh funded by Project SaxoCOV, funded by the German Free State of Saxony. Presentation of data, model results and simulations also funded by the NFDI4Health Task Force COVID19 (https://www.nfdi4health.de/taskforcecovid192) within the framework of a DFGproject (LO342/171). LP, VE funded by Mathematical and Statistical modelling project (MUNI/A/1615/2020), Online platform for realtime monitoring, analysis and management of epidemic situations (MUNI/11/02202001/2020); VE also supported by RECETOX research infrastructure (Ministry of Education, Youth and Sports of the Czech Republic: LM2018121), the CETOCOEN EXCELLENCE (CZ.02.1.01/0.0/0.0/17043/0009632), RECETOX RI project (CZ.02.1.01/0.0/0.0/16013/0001761). NIB funded by Health Protection Research Unit (grant code NIHR200908). SAb, SF funded by Wellcome Trust (210758/Z/18/Z).

 Epidemiology and Global Health
Background:
Affectionate touch, which is vital for mental and physical health, was restricted during the Covid19 pandemic. This study investigated the association between momentary affectionate touch and subjective wellbeing, as well as salivary oxytocin and cortisol in everyday life during the pandemic.
Methods:
In the first step, we measured anxiety and depression symptoms, loneliness and attitudes toward social touch in a large crosssectional online survey (N = 1050). From this sample, N = 247 participants completed ecological momentary assessments over 2 days with six daily assessments by answering smartphonebased questions on affectionate touch and momentary mental state, and providing concomitant saliva samples for cortisol and oxytocin assessment.
Results:
Multilevel models showed that on a withinperson level, affectionate touch was associated with decreased selfreported anxiety, general burden, stress, and increased oxytocin levels. On a betweenperson level, affectionate touch was associated with decreased cortisol levels and higher happiness. Moreover, individuals with a positive attitude toward social touch experiencing loneliness reported more mental health problems.
Conclusions:
Our results suggest that affectionate touch is linked to higher endogenous oxytocin in times of pandemic and lockdown and might buffer stress on a subjective and hormonal level. These findings might have implications for preventing mental burden during social contact restrictions.
Funding:
The study was funded by the German Research Foundation, the German Psychological Society, and German Academic Exchange Service.