Confidence intervals for estimated mean FOI values in simulated scenarios of homogeneous exposure risk, before and during IRS interventions at three different coverage levels.

The times between local transmission events follow a Gamma distribution, with seasonal transmission in a closed system. FOI estimates are derived from true MOI values and MOI estimates obtained through the Bayesian formulation or the bootstrap imputation approach correcting for all or individual sampling limitations. The true mean FOI per host per year is computed by dividing the total number of infections acquired by the population by the total number of hosts in the population. Each boxplot shows minimum, 5% quantile, median, 95% quantile, and maximum values.

Confidence intervals for estimated mean FOI values in simulated scenarios of heterogeneous exposure risk, before and during IRS interventions at three different coverage levels.

The times between local transmission events follow a Gamma distribution, with seasonal transmission in a semi-open system. FOI estimates are derived from true MOI values and MOI estimates obtained through the Bayesian formulation of the varcoding method or the bootstrap imputation approach correcting for all or individual sampling limitations. The true mean FOI per host per year is computed by dividing the total number of infections acquired by the population by the total number of hosts in the population. Each boxplot shows minimum, 5% quantile, median, 95% quantile, and maximum values.

Confidence intervals for the estimated mean FOI values in Ghana surveys before and immediately after a transient three-round IRS intervention

(A) The estimated FOI values when excluding these treated individuals from the analysis. (B) The estimated FOI values when discarding the infection status and MOI estimates of treated individuals and sampling from non-treated ones. Since this case samples non-zero MOIs for these treated and uninfected individuals, it results in an upper bound for FOI estimates. Each boxplot shows minimum, 5% quantile, median, 95% quantile, and maximum. The value of c is set to 30. FOI estimates with other values of c can be found in Appendix 1-Figure 16-18.

The saturation in FOI with increasing EIR and their non-linear relationship from previous field studies.

(A) and (B) present our empirical estimates (with c = 30) when excluding treated individuals from the analysis. (C) and (D) show our estimates when discarding the infection status and MOI estimates of treated individuals and instead sampling from non-treated ones. Since this case samples non-zero MOIs for these treated and uninfected individuals, it results in an upper bound for FOI estimates. The black points represent paired EIR-FOI values from the literature, as summarized by (Smith et al., 2010), with crosses indicating instances where multiple estimates or ranges were reported or estimated for the same location. The red curve represents the best-fit to these paired EIR-FOI values (Smith et al., 2010). The turquoise hollow diamond and plus represent the Ghana data, showing our FOI estimates using the two methods and the EIR measured in the field by the entomological team (Tiedje et al., 2022).

Agent-based model for falciparum malaria transmission.

(A) The stochastic model tracks infection history and specific immune memory of individual hosts to variant surface antigens encoded by var genes. At transmission events, a donor and a recipient host are randomly selected. Transmission occurs if the donor host has blood-stage infections and the recipient host has not reached carrying capacity of infections in its liver. Each parasite genome in the donor host is transmitted to a mosquito with a probability of 1/(number of genomes) multiplied by the transmissibility of the currently expressed gene. Each parasite genome carries 45 var genes, with each gene represented by a linear combination of two epitopes (depicted by different shapes), with many possible variants each (alleles, depicted by different colors). (B) During the sexual stage within mosquitoes, different parasite genomes can exchange var genes through meiotic recombination, generating novel recombinant repertoires. The recipient host can receive either recombinant genomes or original genomes. (C) When a repertoire is successfully transmitted to a recipient host, it undergoes a 7-day dormant liver stage before entering the blood stage, where var genes are sequentially expressed. If the host has no immunity against both epitopes of a var gene, the total duration of expression of the gene lasts 7 days. Immunity against one of the two epitopes shortens the duration of expression by half. Complete immunity against both epitopes results in immediate clearance of the gene product. Infection ends when all var genes in the repertoires are expressed. (D) During the asexual blood stage of infection, var genes within the same genome can swap their two epitope alleles through mitotic (ectopic) recombination, generating new epitopes with a certain probability. (E) Var genes can also mutate their epitopes to create new genes.

(A) Each simulation comprises three stages: a “pre-IRS” period where local transmission reaches a semi-stationary state, followed by a three-year “IRS” intervention period (transient IRS) which reduces transmission rate, and a “post-IRS” period where transmission rates return to original levels. After transmission initialization, closed systems do not receive migrant genomes from the regional pool. Semi-open systems explicitly model two local populations connected by migration. Regionally-open systems continually receive migrant genomes from the regional pool throughout the simulation. (B) Transmission intensity or effective contact rate varies over time, across the pre-, during, and post-intervention periods. We simulate three levels of perturbation coverage, approximately 20% (low-coverage IRS), 40-45% (mid-coverage IRS), and 65-75% (high-coverage IRS) reduction in transmission. (C) We examine different statistical distributions for times between local transmission events: exponential and Gamma. We consider homogeneous and heterogeneous exposure risks. In the latter, of the population are high-risk, receiving approximately 94% of all bites, while the remaining population receives the rest. (D) The measurement error is depicted as a histogram showing the number of non-upsA (i.e., upsB and upsC) DBLα types per repertoire from putatively “monoclonal” infections, characterized by having 45 or fewer non-upsA DBLα types. These sequences were collected during six cross-sectional surveys conducted from 2012 to 2016 in Bongo District. This measurement error represents under-sampling or imperfect detection of var genes. (E) The study consists of four age-stratified cross-sectional surveys in Bongo District, Ghana, conducted at the end of wet/high-transmission seasons (blue circles) and dry/low-transmission seasons (gold circles). Two phases are covered: (1) Pre-IRS: Survey 1 (S1) in October 2012 and Survey 2 (S2) in May/June 2013; (2) Right post-IRS: Survey 3 (S3) in October 2015 and Survey 4 (S4) in May/June 2016. IRS was implemented with widespread LLIN usage distributed between 2010-2012 and again in 2016 (Tiedje et al., 2023; Gogue et al., 2020).

The relationship between the parasitemia level of the individual (measured in uL) and (A) the number of non-upsA var genes per isolate/individual, or (B) MOI estimates from the Bayesian formulation of the varcoding method. There is a lack of association between the x-axis and y-axis variables among both untreated and antimalarial drug-treated individuals. We scale the parasitemia levels and the number of non-ups A var genes or MOI estimates before performing the regression.

Schematic illustration of (A) systems in queuing theory and (B) malaria transmission.

The shape of the negative log likelihood for (A) a simulation run (pre-IRS) with Gamma-distributed times between local transmission events in a seasonal, semi-open system with heterogeneous exposure risk, and (B) Ghana pre-IRS surveys (Survey 1 and 2) with c = 30 and mid PCR detectability. We remove the infinite and extremely large values of the negative log likelihood, and plot the rest to improve visualization.

The impact of grid value choices on the results of FOI inference in either simulated outputs or Ghana data.

By further reducing the grid width to include more combinations of the mean and variance values of inter-arrival times, the FOI inference results remain either unchanged or deviate by no more than 1% from those based on the original grid width.

True and estimated FOI by the two-moment and Little’s Law methods for additional simulated scenarios of homogeneous exposure risk.

The times between local transmission events are Gamma-distributed, with non-seasonal transmission in a closed system. The true mean FOI per host per year is calculated by dividing the total number of infections acquired by the population by the total number of hosts in the population. Each boxplot shows minimum, 5% quantile, median, 95% quantile, and maximum values.

True and estimated FOI by the two-moment and Little’s Law methods for additional simulated scenarios of heterogeneous exposure risk.

The times between local transmission events are Gamma-distributed, with non-seasonal transmission in a semi-open system. The true mean FOI per host per year is calculated by dividing the total number of infections acquired by the population by the total number of hosts in the population. Each boxplot shows minimum, 5% quantile, median, 95% quantile, and maximum values.

True and estimated FOI by the two-moment and Little’s Law methods for additional simulated scenarios of homogeneous exposure risk.

The times between local transmission events are Gamma-distributed, with seasonal transmission in a regionally-open system. The true mean FOI per host per year is calculated by dividing the total number of infections acquired by the population by the total number of hosts in the population. Each boxplot shows minimum, 5% quantile, median, 95% quantile, and maximum values.

True and estimated FOI by the two-moment and Little’s Law for additional simulated scenarios of homogeneous exposure risk.

The times between local transmission events are Gamma-distributed, with non-seasonal transmission in a regionally-open system. The true mean FOI per host per year is calculated by dividing the total number of infections acquired by the population by the total number of hosts in the population. Each boxplot shows minimum, 5% quantile, median, 95% quantile, and maximum values.

True and estimated FOI by the two-moment and Little’s Law methods for additional simulated scenarios of homogeneous exposure risk.

The times between local transmission events follow a exponential distribution, with seasonal transmission in a closed system. The true mean FOI per host per year is calculated by dividing the total number of infections acquired by the population by the total number of hosts in the population. Each boxplot shows minimum, 5% quantile, median, 95% quantile, and maximum values.

Confidence intervals for the estimated mean FOI values in Ghana surveys before and immediately after a transient three-round IRS intervention.

(A) The estimated FOI values when excluding these treated individuals from the analysis. (B) The estimated FOI values when discarding the infection status and MOI estimates of treated individuals and sampling from non-treated ones. Each boxplot shows minimum, 5% quantile, median, 95% quantile, and maximum. The value of c is set to 25.

Confidence intervals for the estimated mean FOI values in Ghana surveys before and immediately after a transient three-round IRS intervention.

(A) The estimated FOI values when excluding these treated individuals from the analysis altogether. (B) The estimated FOI values when discarding the infection status and MOI estimates of treated individuals and sampling from non-treated ones. Each boxplot shows minimum, 5% quantile, median, 95% quantile, and maximum. The value of c is set to 40.

Confidence intervals for the estimated mean FOI values in Ghana surveys before and immediately after a transient three-round IRS intervention.

(A) The estimated FOI values when excluding these treated individuals from the analysis. (B) The estimated FOI values when discarding the infection status and MOI estimates of treated individuals and sampling from non-treated ones. Each boxplot shows minimum, 5% quantile, median, 95% quantile, and maximum. The value of c is set to 60.

Estimated standard deviation of the inter-arrival times using the two-moment approximation method across different simulation scenarios and field data from Bongo District, Ghana.