Changes in transmission of Enterovirus D68 (EV-D68) in England inferred from seroprevalence data

  1. Margarita Pons-Salort  Is a corresponding author
  2. Ben Lambert
  3. Everlyn Kamau
  4. Richard Pebody
  5. Heli Harvala
  6. Peter Simmonds
  7. Nicholas C Grassly
  1. MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College London, United Kingdom
  2. Department of Computer Science, University of Oxford, United Kingdom
  3. Nuffield Department of Medicine, University of Oxford, United Kingdom
  4. Immunization Department, Public Health England, United Kingdom
  5. Infection and Immunity, University College of London, United Kingdom

Abstract

The factors leading to the global emergence of Enterovirus D68 (EV-D68) in 2014 as a cause of acute flaccid myelitis (AFM) in children are unknown. To investigate potential changes in virus transmissibility or population susceptibility, we measured the seroprevalence of EV-D68-specific neutralising antibodies in serum samples collected in England in 2006, 2011, and 2017. Using catalytic mathematical models, we estimate an approximately 50% increase in the annual probability of infection over the 10-year study period, coinciding with the emergence of clade B around 2009. Despite such increase in transmission, seroprevalence data suggest that the virus was already widely circulating before the AFM outbreaks and the increase of infections by age cannot explain the observed number of AFM cases. Therefore, the acquisition of or an increase in neuropathogenicity would be additionally required to explain the emergence of outbreaks of AFM. Our results provide evidence that changes in enterovirus phenotypes cause major changes in disease epidemiology.

Editor's evaluation

The authors use data from three cross-sectional age-stratified serosurveys on Enterovirus D68 from England between 2006 and 2017 to examine the transmission dynamics of this pathogen. This study's convincing methodology provides valuable insights into the changing dynamics of enterovirus D68, uncovering potential changes in the transmissibility of the virus. It will be of interest to infectious disease epidemiologists and surveillance professionals.

https://doi.org/10.7554/eLife.76609.sa0

Introduction

Interest in understanding the epidemiology and disease impact of Enterovirus D68 (EV-D68) and other enteroviruses has increased in recent years. Contrary to most human enteroviruses, EV-D68 causes severe respiratory disease and is transmitted by the respiratory route, sharing properties with rhinoviruses (Oberste et al., 2004). Although this virus was first isolated in 1962, for decades it was only reported from isolated cases or small case clusters of respiratory disease (Pons-Salort et al., 2015).

From 2009 to 2010 onwards however, an increasing number of outbreaks of EV-D68-associated severe respiratory illness have been reported worldwide (Holm-Hansen et al., 2016; Tokarz et al., 2012). In 2014, the US experienced the first big outbreak of respiratory disease linked to EV-D68, with >1100 cases reported by the Centers for Disease Control and Prevention (Midgley et al., 2015). In parallel with this outbreak, an unusual number of acute flaccid myelitis (AFM) cases (a newly recognised condition that includes the sudden onset of flaccid limb weakness [Centers for Disease Control and Prevention, 2021]) were also reported, and similar AFM outbreaks subsequently occurred in 2016 and 2018 (Park et al., 2021). Retrospectively, it now appears, an unusual spike of ‘polio-like’ cases reported in 2012 in California (Ayscue et al., 2014) was an early occurrence of what was subsequently defined as AFM. In the UK and elsewhere in Europe, AFM cases have also been reported in recent years associated with upsurges in EV-D68 detections (Knoester et al., 2019; The United Kingdom Acute Flaccid Paralysis (AFP) Task Force, 2019; Williams et al., 2016). Evidence that EV-D68 is the main cause of these AFM outbreaks has been growing (Park et al., 2021; Messacar et al., 2018), although the role of other enterovirus serotypes such as enterovirus A71 (EV-A71) has not been discounted (McKay et al., 2018). There is no effective treatment or vaccine for EV-D68 infection yet, and residual paralysis and neurological sequelae after AFM is common and lifelong.

The mechanisms that have led to the emergence of EV-D68 outbreaks since the late 2000s remain unknown. One hypothesis is that transmission has increased as a result of evolutionary selection for increased replication fitness, or through the appearance of immune escape-associated mutations that lead to the evasion of pre-existing population immunity. Another is that the virus has become more pathogenic, and, as a consequence, the number of symptomatic (and therefore, reported) infections has increased independently of its transmissibility (i.e. the virus already circulated in the past but went mostly undetected).

As for other enterovirus serotypes, many EV-D68 infections are asymptomatic or mild and self-limiting. In addition, enterovirus surveillance is passive in most countries, based on laboratory reporting for samples submitted by clinicians for testing. It is consequently difficult to determine the true incidence of infection or whether changes in EV-D68 circulation have occurred. A recent study based on data from the BioFire FilmArray Respiratory Panel (Meyers et al., 2020) has shown biennial cycles of EV-D68 circulation in the US at the national level since 2014, coinciding with the years of AFM outbreaks (Park et al., 2021). Similarly, in the UK, reported EV-D68 virus detections also show a biennial pattern between 2014 and 2018 (Figure 1—figure supplement 1). However, these data are limited before 2014 and respiratory samples or throat swabs are infrequently tested by enterovirus surveillance programmes in the US, the UK or elsewhere. Seroprevalence surveys therefore offer an attractive potential alternative opportunity to investigate patterns of exposure to EV-D68. Detection of EV-D68 antibodies with adequate sensitivity and specificity can indicate prior infection and can be analysed using mathematical models to infer trends in the incidence of infection over time, by age-group and location.

Here, we use data on the prevalence of neutralising antibodies against EV-D68 from opportunistically collected serum samples broadly representative of the general population in England in 2006, 2011, and 2017 to reconstruct long-term changes in EV-D68 transmission. Using a mathematical model-based framework, we estimate changes in the annual force of infection (FOI) and reconstruct the estimated annual number of new infections in each age class.

Results

Individuals are assigned an antibody titre as the highest antibody dilution (1:4, 1:8, …, 1:2048) preventing virus replication (i.e. showing neutralisation) (Kamau et al., 2019). For EV-D68, it is unknown which neutralising antibody titre (or seropositivity cut-off) is indicative of true past infection. A simple method to determine a seropositivity cut-off is based on fitting a mixture model to the individual titre distribution, in order to differentiate between two sub-populations (seronegatives and seropositives) (Hens et al., 2012). However, determining such a cut-off was not possible here, as for two of the three serosurveys and for all the data combined, the distributions did not show a bi-modal shape (Figure 1—figure supplement 2). We therefore present our modelling analysis for two different cut-offs: a first weak cut-off of 1:16, which has been previously used in the literature to define EV-D68 seropositivity (Kamau et al., 2019; Karelehto et al., 2019), and a more stringent cut-off of 1:64, which provides seroprevalence curves by age similar to an even more stringent cut-off of 1:128 (Figure 1—figure supplement 3).

Seroprevalence frequencies in different age groups from the three serosurveys of samples collected in 2006, 2011, and 2017 are shown in Figure 1. At each time point, irrespective of the cut-off antibody titre chosen to define seropositivity, seroprevalence slightly decreases from the 0 years-old (yo) to the 1–4 yo age classes, and then increases sharply with age until the 20–29 yo, when it reaches a plateau (Figure 1A, B). As for many other viruses, higher values in the 0-yo age class are likely the result of the presence of transplacentally acquired maternal antibodies that subsequently decline. For a seropositivity cut-off of 1:16, the proportion seropositive at ages 1–4 yo ranged between 0.65 (95% confidence interval [CI] 0.54–0.75) in 2006 and 0.92 (95% CI 0.84–0.97) in 2017. For a more stringent cut-off of 1:64, the proportion seropositive in this age group decreased to 0.29 (95% CI 0.19–0.40) in 2006 and 0.51 (95% CI 0.40–0.62) in 2017. Age-stratified seroprevalence was generally lower in 2006 compared to 2011 and 2017, which suggests individuals acquired their first infection at a lower age through the study period, leading to a decrease in the mean age of exposure. This could potentially be consistent with increased transmission (e.g. through increased viral fitness or the accumulation of susceptible) or other mechanisms (such as a change in the virus to have a higher tendency to infect children).

Figure 1 with 3 supplements see all
Seroprevalence by age.

Seroprevalence by age class in years for the three serosurveys and for two different cut-offs of neutralising antibody titre used to define positivity: (A) 1:16 and (B) 1:64. Seroprevalence by month during the first year of life for children across the three serosurveys combined and two seropositivity cut-offs: (C) 1:16 and (D) 1:64. Bars are 95% binomial confidence intervals. Note that in (A) and (B) individuals in the [0–1) age class from the 2017 serosurvey were in fact sampled in 2016 and as such, are shown with a different colour.

We also explored seroprevalence during the first year of life using data for all children <1 yo across the three serosurveys combined (Figure 1C, D). For both cut-offs, seroprevalence in these children starts very high (92% and 70% for the 1:16 and 1:64 cut-offs, respectively, for children <1 month of age) and declines with age, with a quicker decline during the first 3 months of life then followed by a plateau or slower decline. However, the small number of children per age class resulted in large 95% CIs around the mean. Seroprevalence reaches a minimum at 8 and 4 months of age for the 1:16 and 1:64 cut-offs, respectively. However, the minimum seroprevalence remains high at 50% for the 1:16 cut-off, compared to only 11% for the 1:64.

To address the question of whether transmission had increased before the first reported big outbreaks of EV-D68 in 2014, we compared the performance of two catalytic models that differed on the assumptions of how the FOI changed over time (Materials and methods). Both models assumed that a proportion of individuals are born with maternal antibodies that will subsequently decline at a constant rate, and assumed the risk of infection (becoming seropositive) was independent of age. Model 1 assumed that the FOI was constant over time, and Model 2 allowed it to vary following a random walk. The proportion of individuals born with maternal antibodies was fixed to 1.0 and 0.9 for the seropositivity cut-offs of 1:16 and 1:64, respectively, based on the proportion of adults 25–40 years old that were seropositive in the three serosurveys (Supplementary file 1a).

For both seropositivity cut-offs, Model 2 was the best model according to the leave-one-out (LOO) information criterion (see Materials and methods), which accounts for over-parameterisation (Supplementary file 1b). Model 2 also provided a better fit to the data (Figure 2) than Model 1, which did not capture the observed general increase in seroprevalence between 2006 and 2011 (Figure 2—figure supplement 1). All parameter estimates are presented in Supplementary file 1c.

Figure 2 with 3 supplements see all
Best model fit to data.

Observed (gray) and estimated (blue and red) seroprevalence by age for the three cross-sectional serosurveys (2006, 2011, and 2017). Model fit is shown for the random walk model (Model 2) using the two seropositivity cut-offs, (A) 1:16 and (B) 1:64. Gray intervals indicate the 95% binomial confidence intervals around the observed proportion of seropositivity. The line and ribbons correspond to the median and 95% credible intervals of the posterior estimates of seroprevalence. Note that the age axis is log-transformed to better show the data in the younger age classes. The same plot with the age axis on a natural scale is shown in Figure 2—figure supplement 2. Note also that the data for <1 yo shown for 2017 were actually collected in 2016.

The best model (Model 2) estimated an increase in transmission over time during the study period (2006–2017) for both seropositivity cut-offs, as shown by the estimated FOI in Figure 3A. For the cut-off of 1:16, the FOI continued to increase until the end of the study period, in 2017. However, for the more stringent cut-off of 1:64, the FOI plateaued from around 2011. These differences reflect the differences in seroprevalence observed in the young age classes (1–20 yo) between 2011 and 2017 for the two cut-offs (Figure 1).

Estimates from the best model (Model 2).

Estimated force of infection (FOI) over time (A) and estimated proportion of individuals with detectable maternal antibodies through age (B) for the two seropositivity cut-offs considered. Median and 95% credible intervals are shown for both. In (A), gray arrows indicate the years for which there is cross-sectional seroprevalence data.

There were also important discrepancies in the estimates of the proportion of individuals with maternally acquired antibodies during the first years of life depending on the seropositivity cut-off (Figure 3B). We estimated a quicker decline of maternal antibodies for the more stringent cut-off (1:64), with an estimated median duration of seropositivity due to the presence of maternal antibodies of 4.9 (95% CrI 3.3–7.2) months compared to 17.6 (95% CrI 11.5–26.8) months for the 1:16 cut-off (Figure 3B). Assuming 90% of individuals are born with maternally acquired antibodies for the 1:64 cut-off, this results in a proportion of only 2.3% (95% CrI 0.4–7.4%) of individuals being seropositive due to the presence of maternal antibodies among the 1 yo, compared to 36% (95% CrI 21–51%) for the 1:16 cut-off and 100% of individuals assumed to be born seropositive.

We next used the parameter estimates from the best model and data on the age structure of the population to reconstruct the overall annual EV-D68 seroprevalence in the population (Figure 4) for the period between the first and last cross-sectional serosurveys, 2006–2017. For the two seropositivity cut-offs, the overall seroprevalence was already very high in 2006 (91% [95% CrI 89–93] for 1:16 and 70% [66–74] for 1:64, respectively), and continued to increase progressively until 2017, reaching 97% (96–98%) and 87% (85–89%), respectively, for the 1:16 and 1:64 cut-offs. The detail of the progressive increase in seroprevalence by age year over year as modelled by the random walk is shown in Figure 5A, B.

Overall (age-weighted) seroprevalence per year for the best model using the two different seropositivity cut-offs.

Median and 95% credible intervals are shown.

Changes in the number of infections.

Seroprevalence (A, B) and reconstructed number of infections (C, D) for each age class and year under the best model and for the two seropositivity cut-offs, 1:16 (A, C) and 1:64 (B, D). The insets in (C, D) show the mean age at infection for each year. In (A, B), the median and 95% credible intervals are shown, whereas in (C, D) only the median is shown, for clarity of the plots.

The amount of transmission or extent of virus circulation is better quantified by the number of infections than the FOI, which is sensitive to changes in the age structure of the population (e.g. driven by changes in birth rates) (Tan et al., 2019). Using the best model, we reconstructed the annual number of infections in each age class over time (Figure 5C, D). For both seropositivity cut-offs, the 2-yo age class has the highest annual incidence of infection. The increase in the FOI between 2006 and 2017 results in an increase in the number of infections in the youngest age classes over time, and a decrease in the oldest, with and inflection point around the age of 4–6 yo. This, in turn, results in a decrease in the mean age at infection from 8.5 yo (7.0–10.4) in 2007 to 4.2 yo (3.5–5.1) in 2017 for the 1:16 cut-off, and from 14.3 yo (12.9–15.9) to 9.8 yo (8.9–10.8) for the 1:64.

Discussion

The model-based analysis of individual serological data for EV-D68 from three time points (2006, 2011, and 2017) in England presented here suggests an increase in transmission of EV-D68 that occurred or started before 2011. This coincides with the increased number of outbreaks of EV-D68-associated severe respiratory diseases reported worldwide since the late 2000s (Pons-Salort et al., 2015; Tokarz et al., 2012).

Although our results of an increase in FOI over the study period are robust to the choice of the seropositivity cut-off, we find striking differences in terms of the magnitude of the FOI and the decline of maternal antibodies depending on the seropositivity cut-off used. The results obtained with the more stringent cut-off of 1:64 seem more realistic, both for the estimated annual probabilities of infection (range 0.32–0.52 for the 1:16, and 0.13–0.20 for the 1:64, for the period 2006–2017) and rate of decline of maternal antibodies (average duration of maternal antibodies around 18 mo for the 1:16, and 5 mo for the 1:64). Furthermore, the analysis with the 1:64 cut-off infers that there has not been significant changes in the FOI since 2011; however, with the 1:16 cut-off, the FOI continues to increase until 2017. These results therefore raise the question of what is a suitable seropositivity cut-off to define previous exposure to EV-D68. That said, most EV-D68 seroepidemiology studies published to date present results for a cut-off of 1:8 (as classically used for polioviruses) or 1:16 (Karelehto et al., 2019; Harrison et al., 2019; Sun et al., 2018a; Xiang et al., 2017).

One strength of our analysis is that we account for the decline of maternal antibodies in the catalytic models and are able to estimate the rate of this decline, thanks to the availability of data in the <1 yo. Only one study has reported detailed seroprevalence in the <1 yo (Sun et al., 2018b). This study was conducted in China in 2010, and the data reported are for a seropositivity cut-off of 1:8. Although they found 100% seroprevalence in neonates, close to the observations in our study when using the 1:16 cut-off, this declined to only 28% in the 9–11 months old, which is much lower than the 64% in the same age class in our dataset (Figure 1C). The discrepancy may be partly due to differences in the time of data collection. Indeed, we show data for the three cross-sectional serosurveys combined (2006, 2011, and 2017), given that the number of individuals in each age class was very small, but data for individual years suggest lower seroprevalence in 2006 compared to 2011 and 2017 in the 9–11 mo (Figure 2A).

Our findings point to a clear increase in transmission as measured by the estimated annual probability of infection (approximately, 50% higher in 2017 compared to 2006). However, the reconstructed annual number of new infections in each age class suggests that this increase is mostly driven by an increase in the total number of infections in children aged 1–5 yo. Increased transmission in the youngest age groups may be consistent with observed data showing higher and increasing numbers of respiratory illnesses associated with EV-D68 in these age groups (<5 yo) (Bubba et al., 2020). However, these results on their own are unlikely to explain the worldwide emergence of AFM outbreaks reported since 2014. First, the high overall seroprevalence observed in 2006 suggests that EV-D68 was already widely circulating before 2014. Second, AFM cases do not exclusively or predominantly occur in the youngest age groups. In the US, for example, AFM cases reported in 2014 had a median age of 7.1 yo (interquartile range [IQR], 4.8–12.1 yo) (Sejvar et al., 2016). In the UK, a study from 2018 reported 40 cases, of which only 22 were 0–5 yo (The United Kingdom Acute Flaccid Paralysis (AFP) Task Force, 2019). A study from European countries (2016) reported a median age of cases of 3.8 yo and a range of 1.6–9.0 yo. In Japan, a case series study of an AFM cluster reported an overall median age of cases of 4.4 yo (IQR, 2.6–7.7 yo) (Chong et al., 2018). Although susceptibility to EV-D68-related AFM may vary with age (Hixon et al., 2019) (making it difficult to make a link between the inferred number of infections by age class and the observed number of cases by age), our model-based results suggest that incidence of infections in some of the age groups affected by AFM has not increased, but rather decreased, despite the general increase in transmission. Therefore, the acquisition of or an increase in neuropathogenicity (independent of the described increase in transmission) seems necessary to explain the emergence of AFM through an as-yet unidentified biological mechanism.

The prediction of an increase in the number of infections in the youngest age classes (1–5 yo) is due to the high seroprevalence observed in these age groups (Figure 1) and also the fact that we do not allow for re-infections. As a consequence, only a small number of infections occur at older ages. Although the extremely high seropositivity rates at ages below 5 yo are not generally found with other enteroviruses, they have been reported for EV-D68 in other places (Vogt and Crowe, 2018), for example the US (Harrison et al., 2019), the Netherlands (Karelehto et al., 2019), and China (Sun et al., 2018a; Xiang et al., 2017). Clarifying the origin and the meaning of this high prevalence of neutralising antibodies at this young age (the role of serum neutralising antibodies in protection against infection and diseases) should be a priority for EV-D68 research (Vogt and Crowe, 2018). In particular, it is unclear whether cross-reactivity with other enteroviruses contributes to these high seropositivity and general increase in antibody titres with age (Kamau et al., 2019). If serum neutralising antibodies are not a good correlate of protection against infection, the models may not capture well the age at which infections have increased, and it could be that the increase in infections is across age groups. Indeed, increased transmission may have also been associated with re-infections (and subsequent boosting of antibodies) in older age groups, consistent with the observed rise in geometric mean titres with age (Kamau et al., 2019). However, it seems unlikely that secondary infections can lead to paralysis, based on data for poliovirus.

Whether antigenic escape can explain re-infections in older children is not fully understood. There is evidence of amino acid changes in the BC and DE loop regions of the VP1 (which are thought to be epitopes for neutralising antibodies) that might have resulted in altered antigenic properties (Dyrdak et al., 2019; Imamura et al., 2014). However, although neutralisation assays conducted against different EV-D68 strains found some differences in neutralisation titres, study results have been inconsistent and their clinical and epidemiological significance unclear (Kamau et al., 2019; Harrison et al., 2019).

It is important to interpret well the results for the estimates of the FOI over time from our analysis under the assumptions of the models. First, as the best model uses a random walk on the FOI, the change in transmission that we infer happens continuously over several years. In reality, this may have occurred differently (e.g. in a shorter period of time). Our ability to recover more complex changes in transmission is limited by the data available. It would not be surprising if EV-D68 has exhibited biennial (or longer) cycles of transmission in England over the last few years, as it has been shown in the US (Park et al., 2021) and is common for other enteroviruses (Pons-Salort and Grassly, 2018). However, it is difficult to recover changes at this finer time scale with serology data unless sampling is very frequent (at least annual). Therefore, our study can only reveal broader long-term secular changes. Second, interpretation of the results before 2006 must be avoided for two resasons. On the one hand, as we go backwards in time, there is more uncertaintly about the time of seroconversion of the individuals informing the estimates of the FOI. On the other hand, because age and time are confounded in cross-sectional seroprevalence measurements, the random walk on time may account for possible differences in the FOI through age (possibly higher in the youngest age classes, and lowest in the oldest), which are note explicitly accounted for here. This may explain the decline in FOI when going backwards in time before the first cross-sectional study in 2006. Third, allowing for a higher FOI in younger age classes would result in a shorter duration of maternal antibodies, which would make the results for the 1:16 cut-off more realistic in terms of decline of maternal antibodies. That said, these two parameters (rate of maternal antibodies decline and increase in FOI in younger age classes) would certainly be highly correlated and difficult to be jointly estimated.

Three major co-circulating EV-D68 clades (A–C) emerged globally in the 2000s (Tokarz et al., 2012) and have subsequently diversified, with only one monophyletic group (B1 and B3 genotypes) with a common ancestor in 2009 so far associated with AFM (Hadfield et al., 2018) (with the exception of one case associated with D1 [sometimes called A2] in 2018 in France; Bal et al., 2019). Individual viral lineages show rapid global spread, with recent outbreaks synchronised across Europe and the US representing circulation of the same dominant genotypes. Reported EV-D68 outbreaks in 2014 and 2016 were due to clade B viruses, while the 2018 outbreaks were reported to be linked to both B3 and A2 clade viruses in the UK (The United Kingdom Acute Flaccid Paralysis (AFP) Task Force, 2019), France (Bal et al., 2019), and elsewhere. In vitro studies of the neurotropism of these viruses compared with the ancestral strains have yielded conflicting results as to whether neurotropism has increased (Hixon et al., 2019; Brown et al., 2018; Rosenfeld et al., 2019). The timing of the increase in transmission estimated here (sometime before 2011) based on the analysis of the serology data may roughly correspond to the genetic emergence of clade B around 2007, and thus one could hypothesise that increased virus transmissibility is a trait associated with this clade. More efficient viral replication may enhance transmission as well as the probability of virus reaching the central nervous system, although changes in receptor usage could also play a role.

This work shows the value of modelling age-stratified seroprevalence data from consecutive cross-sectional studies in the understanding of the epidemiology of diseases caused by emerging human enteroviruses. The dynamics of most enterovirus serotypes over relatively long time scales have been shown to be driven by population immunity (Pons-Salort and Grassly, 2018). However, in rare instances, enterovirus serotypes have emerged as important causes of diseases after many years of circulation causing diseases at a much lower rate or even silently circulating. For example, coxsackievirus A6 (CVA6) has emerged as the main serotype causing HFMD worldwide over the last decade (Bian et al., 2015). Finally, this work also shows the need to better understand and interpret individual serological data in terms of previous exposure and protection against infection and disease. This would help refining analytical approaches such as those used here to infer population-level processes.

Materials and methods

Serological data

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We use data from three retrospective cross-sectional studies analysing serum samples representative of England’s population in 2006 (n = 516), 2011 (n = 504), and 2017 (n = 566) and available through the National Seroepidemiology Programme at Public Health England (Osborne et al., 2000). The neutralisation assay method and results from serological testing of the 2006 and 2017 sample sets have been previously described in Kamau et al., 2019. Neutralisation assays measured neutralising antibody titres against a B3 strain (Kamau et al., 2019; Hadfield et al., 2018), but Kamau et al. showed similar neutralisation effects across three different EV-D68 strains (Kamau et al., 2019).

Statistical analysis

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The FOI is the rate at which seronegative (susceptible) individuals become seropositive (infected). Cross-sectional age-stratified seroprevalence data can be used to estimate the FOI through so-called catalytic models (Hens et al., 2010). Catalytic models avoid modelling the dynamics of infected individuals directly; rather, they assume an unspecified mechanism that results in a seronegative individual becoming seropositive, its magnitude defining the FOI. For seroprevalence data, these models rely on the idea that the age and serostatus of an individual provide information on the probability of infection for the years between birth and the serosurvey.

We consider a serocatalytic model with maternal antibodies and no seroreversion (Dighe, 2022). Individuals enter the model at birth either seropositive due to the presence of maternal antibodies (m), or seronegative (n), with maternal antibodies declining at a constant rate ω. Seronegative individuals become seropositive (p) at a rate λ, the FOI. We assume that after seroconversion, individuals cannot become seronegative again; this seems reasonable since seroprevalence does not show a decline through age (Figure 1). This model is described by the following system of differential equations:

dmda=ωm
dnda=ωmλn
dpda=λn

which has the following analytical solution (Dighe, 2022):

ma=m0e-ωa
n(a)=m0(ωλω(eωaeλa))+(1m0)eλa
pa=1-ma-na

where m0 is the proportion of individuals born with maternal antibodies, that we consider fixed and constant over time.

We are interested in estimating the rate of waning of maternal antibodies, ω, and the FOI, λ. To link the catalytic model to the data from the serosurveys, we assume that the count of seropositive individuals within a serosurvey in year t follows a binomial distribution:

zτ(t|c) binomial(nτ(t),mτ(t)+pτ(t)),

where nτt indicates the sample size in year t for individuals born in year τ, tτ, as collected during the serosurvey, and zτ(t|c) is the count of those who are seropositive for a given cut-off c . The sum mτt+pτt is the modelled proportion seropositive at year t among those who were born in year τ. Note that we further assume that testing uncovers seropositivity with 100% accuracy.

We test two different models representing different hypotheses about how the FOI changes over time t. Model 1 assumes a constant FOI over time,

λt=λ,t.

And Model 2 allows the FOI to change over time following a random walk of order one:

λt=t1 normal(0,0.5)
λt>t1 normal(λt1,σ)

Both models assume a constant FOI through age.

The annual probability of infection, which is the proportion of the susceptible population that will become seropositive in a given year t, can be derived from the FOI: p(t)=1exp(λ(t)) .

Because seroprevalence in adults reaches almost 100% from about the 20-yo age class for a seropositivity cut-off of 1:16, and from the 30-yo for a more stringent cut-off of 1:64 (Figure 1), we fit the models to the data for age up to 40 yo.

The models were implemented in Stan Development Team, 2020 and fitted to the data using MCMC. Four independent chains were simulated, each of 10,000 iterations, with a warmup of 3,000. Convergence was checked using the Rhat function.

We use the LOO metrics (Vehtari et al., 2017), implemented in the ‘loo’ R package (Vehtari et al., 2023), for model comparison. The LOO metrics aim to gauge how well a model generalises to an out-of-sample dataset and are an approximation to the explicit LOO cross-validation log-likelihood. In the explicit approach, the model is fitted to n − 1 datapoints and tested on a single hold-out datapoint and the log-likelihood on the test datapoint recorded. This approach is repeated for each of n datapoints. The LOO is then effectively the average log-likelihood across all held-out datapoints. The ‘loo’ package uses Pareto-smoothed importance sampling to avoid explicitly refitting the model to the data n times.

Annual overall seroprevalence and reconstructed number of infections in each age class

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Using the estimates of the FOI from the catalytic models above and data on population structure, we can estimate the overall (age-weighted) seroprevalence in the population each year t. We used data on the population structure in England for the years 1998, 2008, and 2018 from Office for National Statistics, 2020. The size of each age class for the years in between was obtained by linear interpolation.

Finally, we reconstructed the annual number of (new) infections in each age class using the estimates of the FOI and population structure data. To reconstruct the number of infections in a given year t and age class a, we first reconstructed the proportion seronegative in the age class a − 1 until year t − 1, and then derived the proportion who would seroconvert during year t. We then multiplied that proportion by the population size of the corresponding age class and year.

Code and data are available through the GitHub repository: https://github.com/margapons/EV-D68_seroprevalence_England, (copy archived at Pons-Salort, 2023).

Data availability

Data analysed in this study are available through a GitHub repository.

The following data sets were generated

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Decision letter

  1. Isabel Rodriguez-Barraquer
    Reviewing Editor; University of California, San Francisco, United States
  2. Eduardo L Franco
    Senior Editor; McGill University, Canada

Our editorial process produces two outputs: (i) public reviews designed to be posted alongside the preprint for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.

Decision letter after peer review:

Thank you for submitting your article "Changes in transmission of Enterovirus D68 (EV-D68) in England inferred from seroprevalence data" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The reviewers have opted to remain anonymous.

As is customary in eLife, the reviewers have discussed their critiques with one another. What follows below is the Reviewing Editor's edited compilation of the essential and ancillary points provided by reviewers in their critiques and in their interaction post-review. Please submit a revised version that addresses these concerns directly. Although we expect that you will address these comments in your response letter, we also need to see the corresponding revision clearly marked in the text of the manuscript. Some of the reviewers' comments may seem to be simple queries or challenges that do not prompt revisions to the text. Please keep in mind, however, that readers may have the same perspective as the reviewers. Therefore, it is essential that you attempt to amend or expand the text to clarify the narrative accordingly.

Essential revisions:

The authors use data from 3 cross-sectional age-stratified serosurveys on Enterovirus D68 from England between 2006 and 2017 to examine the transmission dynamics of this pathogen in this setting. Understanding these dynamics, including how it changes over time, may help uncover potential changes in the transmissibility of the virus. While the topic is relevant, interpretation of the results challenging largely due to the great uncertainty around how to interpret the serological (serostatus) data, and the impact this has on the inferences made. We ask the authors to perform some additional analyses and to provide more intuition to understand some of the key findings of this analysis.

1. We struggle to reconcile the evidence of a stable or even small drop in FoI after 2010 in the 1:64 models in contrast to the continued increase using the 1:16 cut-point.

2. It is hard to reconcile evidence of drops in FoI in the 1:64 (models 4 and 5 from 2010/11 (Figure 3)) with steadily increasing R0 in this period (Figure 4). Is this due to changes in the susceptibility proportion. It would be good to understand if there are important assumptions in the Farrington approach that may also contribute to this discrepancy.

3. One of the major findings of the paper is that there is a steadily increasing R0 (using the 1:64 cut-point). This again is difficult to understand and would suggest there are either year on year increases in inherent transmissibility of the virus through fitness changes, or year on year increases in the mixing of the population. It would be useful for the authors to discuss potential explanations for an inferred gradual increase in R0.

4.The estimated FOI in 1 year olds is very very high (with a suggestion that up to 75% get infected within a year) and difficult to believe, especially as the force of infection is assumed much lower for all other ages. The authors exclude all <1s due to maternal antibodies, which seems sensible, however, does this mean that it is impossible for <1s to become infected in the model? We know for other pathogens (e.g., dengue virus) with protection from maternal antibodies that the protection from infection is gone after a few months. Maybe allowing for infections in the first year of life too would reduce the very large, and difficult to believe, difference in risk between 1 year olds and older age groups. I suspect you wouldn't need to rely on <1 serodata – just allow for infections in this time period.

5. Relatedly would it be possible to break the age data into months rather than years in these infants to help tease apart what happens in the critical early stages of life.

6. Additional context of EV-D68 in the study setting of England would be useful. While the Introduction does mention AFM cases "in the UK and elsewhere in Europe" (line 53), a summary of reported data on EV-D68/AFM in England prior to this study would provide important context. The Methods refers to "whether transmission had increased over time (before the first reported big outbreak of EV-D68 in the US in 2014)" (lines 133-134), rather than in this setting. It would be useful to summarize the viral genomic data from the region for additional context – particularly since the emergence of a viral clade is highlighted as a co-occurrence with the increased transmissibility detected in this analysis.

7. Given the substantial uncertainty in the assay, it seems optimistic to attempt to fit annual force of infections in the 30 year period prior to the start of the sampling periods. Authors should consider including a constant λ prior to the dates of the first study across the models considered.

8. While the authors have made data sets available, it would be good to make computer code available as well.

Reviewer #1 (Recommendations for the authors):

In the abstract it would be helpful to have some info on the AFM in England as a link between the global picture explained and then this analysis which is for England.

Line 188-120: I agree with the point here, but wonder if a little more to be added to help guide the reader through this thinking from lower seroprevelance to age. I also wonder if it isn't due to an increase in transmission what is it due to? Perhaps this could also be elaborated on.

Line 169 (and methods): Please provide more information on the LOO criteria and what was left out. More required in the main text and also in the methods.

Reviewer #2 (Recommendations for the authors):

– The submission lists only 2 contributing authors, but the manuscript lists additional authors. The author lists should be synced.

– While the authors have made data sets available, computer code was not available as far as I could tell.

– For Models 4 and 5: what were the estimated values of sigma0 and σ? They were not included in Table S1. In the Methods section, λ_{t=t1} is modeled as a Normal centered at 0 – is this on the log scale?

– Figure 2 (E and F): what does the purple class indicate for this model? Is it an average across all other age classes?

– Table 1: it was not clear why Model 3's δ LOO is so poor compared to Model 5 despite the similar visual fits of the models (Figure 3 vs. Figure S5), particularly among the under 20 year-olds. Could the authors provide some more intuition on this? Are there particular data points that are highly influential on the LOO statistic?

– Line 142: should this sentence also include γ?

– Lines 159-167: the values cited in the text do not seem to match those in Table S1.

– Line 172: what do these p-values represent?

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Changes in transmission of Enterovirus D68 (EV-D68) in England inferred from seroprevalence data" for further consideration by eLife. Your revised article has been evaluated by Eduardo Franco (Senior Editor) and a Reviewing Editor.

The manuscript has been improved, but there are a couple of issues that need to be addressed, as outlined below (see comments from reviewer #4)

Reviewer #4 (Recommendations for the authors):

I have two comments on the revision:

1. I agree with the authors' decision to implement maternal antibodies as part of their modeling approach. However, the estimated proportion of individuals with maternal antibodies by age seems very high for the 1:16 cutoff. Is it realistic to have maternal antibodies in >25% of 2 year olds? If not, it might be prudent to have m(a) go to zero by a certain age.

2. I had made a comment in the previous round of review about extending the x-axis to the start of the time period of estimation: this was in reference to FOI, not seroprevalence. The FOI estimates in Figure 3A begin in 1990, but the oldest cohort in this analysis are 40 y in 2006, and it's not clear what is assumed about FOI between 1966 and 1990. Or does the random walk on the FOI begin in 1966? It would be good to show those results.

https://doi.org/10.7554/eLife.76609.sa1

Author response

Essential revisions:

The authors use data from 3 cross-sectional age-stratified serosurveys on Enterovirus D68 from England between 2006 and 2017 to examine the transmission dynamics of this pathogen in this setting. Understanding these dynamics, including how it changes over time, may help uncover potential changes in the transmissibility of the virus. While the topic is relevant, interpretation of the results challenging largely due to the great uncertainty around how to interpret the serological (serostatus) data, and the impact this has on the inferences made. We ask the authors to perform some additional analyses and to provide more intuition to understand some of the key findings of this analysis.

We have changed the order of the comments, to describe first the main changes to the manuscript and make the explanations clearer.

5. Relatedly would it be possible to break the age data into months rather than years in these infants to help tease apart what happens in the critical early stages of life.

Yes. We have added two figures (new Figures 1C and 1D) showing the prevalence of antibodies in children <1 yo. We show these data for the three serosurveys combined, because the number of individuals per month of age is very small.

4.The estimated FOI in 1 year olds is very very high (with a suggestion that up to 75% get infected within a year) and difficult to believe, especially as the force of infection is assumed much lower for all other ages. The authors exclude all <1s due to maternal antibodies, which seems sensible, however, does this mean that it is impossible for <1s to become infected in the model? We know for other pathogens (e.g., dengue virus) with protection from maternal antibodies that the protection from infection is gone after a few months. Maybe allowing for infections in the first year of life too would reduce the very large, and difficult to believe, difference in risk between 1 year olds and older age groups. I suspect you wouldn't need to rely on <1 serodata – just allow for infections in this time period.

We thank the reviewers for this important suggestion. We have changed the catalytic models and now use a model that includes individuals with maternal antibodies at birth. With this new model, we no longer need to make extra hypothesis about differences in FOI at age 1. We now estimate both the rate of decline of maternal antibodies and the FOI (that we assume constant through age). We have substantially revised the Methods section to describe the new approach, updated all the results accordingly. These includes the model fit (new Figure 2) and the estimates of the FOI over time (new Figure 3A). We also show the decline of the estimated proportion of individuals with maternal antibodies through age (new Figure 3B).

1. We struggle to reconcile the evidence of a stable or even small drop in FoI after 2010 in the 1:64 models in contrast to the continued increase using the 1:16 cut-point.

With the new model (i.e. with maternal antibodies) the difference in the “trajectory” of the FOI over time for the two cut-off persists. We think this is driven by the difference in seroprevalence between the youngest age classes in 2011 vs. 2017 for the two cut-offs (see Figures 1A and 1B). For the 1:16 cut-off, seroprevalence in the young age classes increases over time between the first serosurvey in 2006 and the last one in 2017 (Figure 1A). However, for the 1:64 cut-off, seroprevalence in the young age classes is very similar for the 2011 and 2017 serosurveys. The serocatalytic models therefore do not estimate a change in the FOI between those two time points.

We thank the reviewers for highlighting this point, which we did not discuss before. We have now added the following text to the Results:

“The best model (Model 2) estimated an increase in transmission over time during the study period (2006-2017) for both seropositivity cut-offs, as shown by the estimated FOI in Figure 3A. For the cut-off of 1:16, the FOI continued to increase until the end of the study period, in 2017. However, for the more stringent cut-off of 1:64, the FOI plateaued from around 2011. These differences reflect the differences in seroprevalence observed in the young age classes (1 – 20 yo) between 2011 and 2017 for the two cut-offs (Figure 1).”

And we have also added the following paragraph to the Discussion presenting the main differences in the results for the two cut-offs:

“Although our results of an increase in FOI over the study period are robust to the choice of the seropositivity cut-off, we find striking differences in terms of the magnitude of the FOI and the decline of maternal antibodies depending on the seropositivity cut-off used. The results obtained with the more stringent cut-off of 1:64 seem more realistic, both for the estimated annual probabilities of infection (range 0.32-0.52 for the 1:16, and 0.13-0.20 for the 1:64, for the period 2006-2017) and rate of decline of maternal antibodies (average duration of maternal antibodies around 18 mo for the 1:16, and 5 mo for the 1:64). Furthermore, the analysis with the 1:64 cut-off infers that there has not been significant changes in the FOI since 2011; however, with the 1:16 cut-off, the FOI continuous to increase until 2017. These results therefore raise the question of what is a suitable seropositivity cut-off to define previous exposure to EV-D68. That said, most EV-D68 seroepidemiology studies published to date present results for a cut-off of 1:8 (as classically used for polioviruses) or 1:16 (17, 19-21).”

2. It is hard to reconcile evidence of drops in FoI in the 1:64 (models 4 and 5 from 2010/11 (Figure 3)) with steadily increasing R0 in this period (Figure 4). Is this due to changes in the susceptibility proportion. It would be good to understand if there are important assumptions in the Farrington approach that may also contribute to this discrepancy.

We have removed the estimates of R0 from the manuscript and only present the reconstruction of the annual number of new infections per age class and year (new Figure 5). We think this measure is more adapted to the discussion of the results.

In addition, when using the classical expression R{0t}=1/(1-S(t)), with S(t) the annual proportion seropositive, the high seroprevalence estimates (new Figure 4) result in extremely high estimates of the basic reproduction number (median ranges: 11.6 – 29.7 for 1:16 and 3.3 – 7.6 for 1:64 during the period 2006 to 2017).

We had previously used the Farrington approach as it is adapted to cases when the force of infections is different for different age classes.

3. One of the major findings of the paper is that there is a steadily increasing R0 (using the 1:64 cut-point). This again is difficult to understand and would suggest there are either year on year increases in inherent transmissibility of the virus through fitness changes, or year on year increases in the mixing of the population. It would be useful for the authors to discuss potential explanations for an inferred gradual increase in R0.

We have removed the estimates of R0 from the manuscript.

6. Additional context of EV-D68 in the study setting of England would be useful. While the Introduction does mention AFM cases "in the UK and elsewhere in Europe" (line 53), a summary of reported data on EV-D68/AFM in England prior to this study would provide important context. The Methods refers to "whether transmission had increased over time (before the first reported big outbreak of EV-D68 in the US in 2014)" (lines 133-134), rather than in this setting. It would be useful to summarize the viral genomic data from the region for additional context – particularly since the emergence of a viral clade is highlighted as a co-occurrence with the increased transmissibility detected in this analysis.

We have added a figure (new Figure 1 —figure supplement 1) showing the annual number of EV-D68 detections reported by Public Health England from 2004 to 2020.

We have also added the following text to the introduction: “Similarly, in the UK, reported EV-D68 virus detections also show a biennial pattern between 2014 and 2018 (Figure 1 —figure supplement 1).”

We have also amended the sentence in the Methods.

Finally, Author response image 1 is a screenshot of the nexstrain tree for EV-D68 based on the VP1 region and with tips representing sequences from the UK (light blue) and European countries in colour. There is a lot of mixing between sequences from different regions, indicating widespread transmission and small regional clustering. We have added the following text to the Discussion: “Reported EV-D68 outbreaks in 2014 and 2016 were due to clade B viruses, while the 2018 outbreaks were reported to be linked to both B3 and A2 clade viruses in the UK (10), France (32) and elsewhere.”

Author response image 1

7. Given the substantial uncertainty in the assay, it seems optimistic to attempt to fit annual force of infections in the 30 year period prior to the start of the sampling periods. Authors should consider including a constant λ prior to the dates of the first study across the models considered.

We thank the reviewers for the suggestion.

We implemented this change (constant FOI before 2006) in the previous models without maternal antibodies and the result for the random-walk-based models was that the variance of the random walk was estimated over a very short period, thus resulting in a rather nonsmoothed FOI.

Implementing this change with the new models with maternal antibodies and random-walk on the FOI was technically a bit complex. We therefore kept the simple random-walk over the whole period and added the following paragraph to the Discussion:

“It is important to interpret well the results for the estimates of the FOI over time from our analysis under the assumptions of the models. First, as the best model uses a random walk on the FOI, the change in transmission that we infer happens continuously over several years. In reality, this may have occurred differently (e.g. in a shorter period of time). Our ability to recover more complex changes in transmission is limited by the data available. It would not be surprising if EV-D68 has exhibited biennial (or longer) cycles of transmission in England over the last few years, as it has been shown in the US (7) and is common for other enteroviruses (30). However, it is difficult to recover changes at this finer time scale with serology data unless sampling is very frequent (at least annual). Therefore, our study can only reveal broader long-term secular changes. Second, interpretation of the results before 2006 must be avoided for two reasons. On the one hand, as we go backwards in time, there is more uncertainty about the time of seroconversion of the individuals informing the estimates of the FOI. On the other hand, because age and time are confounded in cross sectional seroprevalence measurements, the random walk on time may account for possible differences in the FOI through age (possibly higher in the youngest age classes, and lowest in the oldest), which are note explicitly accounted for here. This may explain the decline in FOI when going backwards in time before the first cross-sectional study in 2006.”

8. While the authors have made data sets available, it would be good to make computer code available as well.

The code is available in the GitHub repo: https://github.com/margapons/EVD68_seroprevalence_England

Reviewer #1 (Recommendations for the authors):

In the abstract it would be helpful to have some info on the AFM in England as a link between the global picture explained and then this analysis which is for England.

Data for AFM is scarce for England and publications do not always allow to discern the overlap of cases reported nor to differentiate between cases of AFP (acute flaccid paralysis) and AFM (acute flaccid myelitis) – the last one being defined only in 2014. A ballpark estimate for the number of AFM cases in the UK is in the range of 20-30, between January 2015 and December 2018, based on data reported in publications (1-5) below. As this number is not precise, nor confirmed by health authorities, we prefer not to report it. Note, however, that now we do report number of EV-D68 detections in the UK.

1. Kirolos, A., et al., Outcome of paediatric acute flaccid myelitis associated with enterovirus D68: a case series. Dev Med Child Neurol, 2019. 61(3): p. 376-380.

2. Cottrell, S., et al., Prospective enterovirus D68 (EV-D68) surveillance from September 2015 to November 2018 indicates a current wave of activity in Wales. Euro Surveill, 2018. 23(46).

3. Williams, C.J., et al., Cluster of atypical adult Guillain-Barre syndrome temporally associated with neurological illness due to EV-D68 in children, South Wales, United Kingdom, October 2015 to January 2016. Euro Surveill, 2016. 21(4).

4. Bubba, L., et al., Circulation of non-polio enteroviruses in 24 EU and EEA countries between 2015 and 2017: a retrospective surveillance study. Lancet Infect Dis, 2020. 20(3): p. 350-361.

5. The United Kingdom Acute Flaccid Paralysis Afp Task, F., An increase in reports of acute flaccid paralysis (AFP) in the United Kingdom, 1 January 2018-21 January 2019: early findings. Euro Surveill, 2019. 24(6).

Line 188-120: I agree with the point here, but wonder if a little more to be added to help guide the reader through this thinking from lower seroprevelance to age. I also wonder if it isn't due to an increase in transmission what is it due to? Perhaps this could also be elaborated on.

Thanks for this suggestion. We agree with the reviewer that the previous formulation was unclear. These now reads:

“Age-stratified seroprevalence was generally lower in 2006 compared to 2011 and 2017, which suggests individuals acquired their first infection at a lower age through the study period, leading to a decrease in the mean age of exposure. This could potentially be consistent with increased transmission (e.g. through increased virus fitness or the accumulation of susceptible) or other mechanisms (such as a change in the virus to have a higher tendency to infect children).”

Line 169 (and methods): Please provide more information on the LOO criteria and what was left out. More required in the main text and also in the methods.

The LOO metrics aim to gauge how well a model generalises to an out-of-sample dataset and are an approximation to the explicit leave-one out cross-validation log-likelihood (Vehtari, Gelman and Gabry, 2017). In the explicit approach, the model is fitted to n-1 datapoints and tested on a single hold-out datapoint and the log-likelihood on the test datapoint recorded. This approach is repeated for each of n datapoints. The LOO is then effectively the average log-likelihood across all held-out datapoints (accounting for uncertainty in the posterior).

We used the “loo” R package (Vehtari et al., 2022) to calculate the LOO metric, which uses Pareto-smoothed importance sampling to avoid explicitly refitting to the data n times. This metric and the method for its approximation are widely used in applied Bayesian inference for performing model comparison.

Vehtari A, Gelman A, and Gabry J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and computing (2017): 1413-1432.

Vehtari A, Gabry J, Magnusson M, Yao Y, Bürkner P, Paananen T, Gelman A (2022). “loo: Efficient leave-one-out cross-validation and WAIC for Bayesian models.” R package version 2.5.1, https://mc-stan.org/loo/

We have now added the following text to the Methods:

We use the LOO metrics (39), implemented in the “loo” R package (40), for model comparison. The LOO metrics aim to gauge how well a model generalises to an out-of-sample dataset and are an approximation to the explicit leave-one-out cross-validation loglikelihood. In the explicit approach, the model is fitted to n-1 datapoints and tested on a single hold-out datapoint and the log-likelihood on the test datapoint recorded. This approach is repeated for each of n datapoints. The LOO is then effectively the average loglikelihood across all held-out datapoints. The “loo” package uses Pareto-smoothed importance sampling to avoid explicitly refitting the model to the data n times.

Reviewer #2 (Recommendations for the authors):

– The submission lists only 2 contributing authors, but the manuscript lists additional authors. The author lists should be synced.

The manuscript has 7 authors (listed in the pdf file). It is unclear to us why the submission showed only two.

– While the authors have made data sets available, computer code was not available as far as I could tell.

The code is available in the GitHub repo https://github.com/margapons/EVD68_seroprevalence_England

– For Models 4 and 5: what were the estimated values of sigma0 and σ? They were not included in Table S1. In the Methods section, λ_{t=t1} is modeled as a Normal centered at 0 – is this on the log scale?

We have now conducted a sensitivity analysis and seen that the value of sigma0 does not affect the estimates. We therefore fix sigma0 = 0.5, and only estimate σ. The Methods section has been updated accordingly and we also provide the estimates of σ and other parameters in the new Table S3.

The prior of λ_{t=t1} is a Normal distribution centered at 0 (in the natural scale; not log scale) restricted to positive values (a “half-normal” distribution). It is effectively truncated at zero, as we set the lower bound for this parameter at zero.

– Figure 2 (E and F): what does the purple class indicate for this model? Is it an average across all other age classes?

This comment does no longer apply, as the models have changed.

– Table 1: it was not clear why Model 3's δ LOO is so poor compared to Model 5 despite the similar visual fits of the models (Figure 3 vs. Figure S5), particularly among the under 20 year-olds. Could the authors provide some more intuition on this? Are there particular data points that are highly influential on the LOO statistic?

This comment does no longer apply, as the models have changed.

– Line 142: should this sentence also include γ?

This comment does no longer apply, as the models have changed and there is no parameter γ.

– Lines 159-167: the values cited in the text do not seem to match those in Table S1.

This comment does no longer apply, as the models have changed.

– Line 172: what do these p-values represent?

These p-values represent the probability that the null hypothesis that two models provide the same fit to the data is true (vs the alternative that one model outperforms the other). The p-values are calculated under a normal approximation of the ELPD measure of fit as discussed in (Vehtari, Gelman and Gabry, 2017).

As the differences in ELPD between the two new models (constant and the random-walk) are large for the two datasets, we no longer present these p-values, which we understand may not be straightforward to interpret for the reader.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

The manuscript has been improved, but there are a couple of issues that need to be addressed, as outlined below (see comments from reviewer #4)

Reviewer #4 (Recommendations for the authors):

I have two comments on the revision:

1. I agree with the authors' decision to implement maternal antibodies as part of their modeling approach. However, the estimated proportion of individuals with maternal antibodies by age seems very high for the 1:16 cutoff. Is it realistic to have maternal antibodies in >25% of 2 year olds? If not, it might be prudent to have m(a) go to zero by a certain age.

We agree with the reviewer that the estimate of >25% of individuals with maternal antibodies by the age of 2 yo obtained for the 1:16 cut-off seems unrealistic. Actually, we believe that all the results (including also FOI estimates) are more realistic for the 1:64 cutoff than for the 1:16, and we already discuss this in the second paragraph of the Discussion. We think it is important to show the results obtained with both cut-offs, as studies reporting EVD68 seroprevalence published so far have used a seropositivity cut-off of 1:8 or 1:16, which we think may not be the most suitable for this enterovirus serotype.

A main observation of our and other studies is that seroprevalence is very high in the 12-23 months old for the 1:16 cut-off and this is discussed at several points in the Discussion. In our approach, the rate of decline of maternal antibodies (parameter omega) is estimated, and therefore, informed by the seroprevalence data. If we fixed it and “forced it to go to zero by a certain age”, as suggested by the reviewer, we would need to consider a higher FOI in the younger age classes to be able to explain the high seroprevalence observed in those. We have now added the following sentence to the Discussion to acknowledge the limitation:

“Third, allowing for a higher FOI in younger age classes would result in a shorter duration of maternal antibodies, which would make the results for the 1:16 cut-off more realistic in terms of decline of maternal antibodies. That said, these two parameters (rate of maternal antibodies decline and increase in FOI in younger age classes) would certainly be highly correlated and difficult to be jointly estimated.”

2. I had made a comment in the previous round of review about extending the x-axis to the start of the time period of estimation: this was in reference to FOI, not seroprevalence. The FOI estimates in Figure 3A begin in 1990, but the oldest cohort in this analysis are 40 y in 2006, and it's not clear what is assumed about FOI between 1966 and 1990. Or does the random walk on the FOI begin in 1966? It would be good to show those results.

The random walk starts at 1966. The figure with the complete estimate of the FOI over time is shown in Author response image 2:

Author response image 2

We prefer not to show the FOI estimates for the initial period for two reasons. First, we are interested on seeing whether there has been an increase in transmission in the few years before the first large EV-D68 outbreaks in 2014. This is, between a few years before 2006 (our first time point with data) and 2014. Second, because our first time point of observations is 2006 and seroprevalence increases quickly with age, the FOI estimates going backwards in time are informed by older, mostly seropositive individuals, which results in a basically flat or not well estimated FOI. This is clearer for the 1:16 cut-off, for which we observe a large increase in the credible intervals. This is because seroprevalence quickly reaches 100% (around the age of 20) and therefore, there is not much signal in the data to inform the FOI going backwards in time, i.e. before 2006-20=1986 approximately.

https://doi.org/10.7554/eLife.76609.sa2

Article and author information

Author details

  1. Margarita Pons-Salort

    MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College London, London, United Kingdom
    Contribution
    Conceptualization, Formal analysis, Investigation, Visualization, Methodology, Writing - original draft
    For correspondence
    m.pons-salort@imperial.ac.uk
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-5597-9285
  2. Ben Lambert

    Department of Computer Science, University of Oxford, Oxford, United Kingdom
    Contribution
    Methodology, Writing - review and editing
    Competing interests
    No competing interests declared
  3. Everlyn Kamau

    Nuffield Department of Medicine, University of Oxford, Oxford, United Kingdom
    Contribution
    Data curation, Writing - review and editing
    Competing interests
    No competing interests declared
  4. Richard Pebody

    Immunization Department, Public Health England, London, United Kingdom
    Contribution
    Resources, Writing - review and editing
    Competing interests
    No competing interests declared
  5. Heli Harvala

    Infection and Immunity, University College of London, London, United Kingdom
    Contribution
    Resources, Writing - review and editing
    Competing interests
    No competing interests declared
  6. Peter Simmonds

    Nuffield Department of Medicine, University of Oxford, Oxford, United Kingdom
    Contribution
    Resources, Writing - review and editing
    Competing interests
    No competing interests declared
  7. Nicholas C Grassly

    MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College London, London, United Kingdom
    Contribution
    Writing - review and editing
    Competing interests
    No competing interests declared

Funding

Wellcome Trust (216427/Z/19/Z)

  • Margarita Pons-Salort

Wellcome Trust (ISSF204826/Z/16/Z)

  • Peter Simmonds

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

We want to thank Sang Woo Park (Princeton University) for insightful comments to an initial version of the manuscript. MP-S is a Sir Henry Dale Fellow jointly funded by the Wellcome Trust and the Royal Society (grant number 216427/Z/19/Z). MP-S and NCG acknowledge funding from the MRC Centre for Global Infectious Disease Analysis (reference MR/R015600/1), jointly funded by the UK Medical Research Council (MRC) and the UK Foreign, Commonwealth & Development Office (FCDO), under the MRC/FCDO Concordat agreement and is also part of the EDCTP2 programme supported by the European Union. Work in PS’s lab was supported by a Wellcome ISSF grant (ISSF204826/Z/16/Z). We thank the PHE Sero-Epidemiology Unit for access to residual samples for this public health investigation.

Senior Editor

  1. Eduardo L Franco, McGill University, Canada

Reviewing Editor

  1. Isabel Rodriguez-Barraquer, University of California, San Francisco, United States

Version history

  1. Preprint posted: November 9, 2021 (view preprint)
  2. Received: December 22, 2021
  3. Accepted: May 29, 2023
  4. Version of Record published: June 9, 2023 (version 1)

Copyright

© 2023, Pons-Salort 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.

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  1. Margarita Pons-Salort
  2. Ben Lambert
  3. Everlyn Kamau
  4. Richard Pebody
  5. Heli Harvala
  6. Peter Simmonds
  7. Nicholas C Grassly
(2023)
Changes in transmission of Enterovirus D68 (EV-D68) in England inferred from seroprevalence data
eLife 12:e76609.
https://doi.org/10.7554/eLife.76609

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https://doi.org/10.7554/eLife.76609

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    Large reductions in the global malaria burden have been achieved, but plateauing funding poses a challenge for progressing towards the ultimate goal of malaria eradication. Using previously published mathematical models of Plasmodium falciparum and Plasmodium vivax transmission incorporating insecticide-treated nets (ITNs) as an illustrative intervention, we sought to identify the global funding allocation that maximized impact under defined objectives and across a range of global funding budgets. The optimal strategy for case reduction mirrored an allocation framework that prioritizes funding for high-transmission settings, resulting in total case reductions of 76% and 66% at intermediate budget levels, respectively. Allocation strategies that had the greatest impact on case reductions were associated with lesser near-term impacts on the global population at risk. The optimal funding distribution prioritized high ITN coverage in high-transmission settings endemic for P. falciparum only, while maintaining lower levels in low-transmission settings. However, at high budgets, 62% of funding was targeted to low-transmission settings co-endemic for P. falciparum and P. vivax. These results support current global strategies to prioritize funding to high-burden P. falciparum-endemic settings in sub-Saharan Africa to minimize clinical malaria burden and progress towards elimination, but highlight a trade-off with ‘shrinking the map’ through a focus on near-elimination settings and addressing the burden of P. vivax.