From multiplicity of infection to force of infection for sparsely sampled Plasmodium falciparum populations at high transmission.

High multiplicity of infection or MOI, the number of genetically distinct parasite strains co-infecting a single human host, characterizes infectious diseases including falciparum malaria at high transmission. It accompanies high asymptomatic Plasmodium falciparum prevalence despite high exposure, creating a large transmission reservoir challenging intervention. High MOI and asymptomatic prevalence are enabled by immune evasion of the parasite achieved via vast antigenic diversity. Force of infection or FOI, the number of new infections acquired by an individual host over a given time interval, is the dynamic sister quantity of MOI, and a key epidemiological parameter for monitoring the impact of antimalarial interventions and assessing vaccine or drug efficacy in clinical trials. FOI remains difficult, expensive, and labor-intensive to accurately measure, especially in high-transmission regions, whether directly via cohort studies or indirectly via the fitting of epidemiological models to repeated cross-sectional surveys. We propose here the application of queuing theory to obtain FOI on the basis of MOI, in the form of either a two-moment approximation method or Little's law. We illustrate these methods with MOI estimates obtained under sparse sampling schemes with the recently proposed " var coding" method, based on sequences of the var multigene family encoding for the major variant surface antigen of the blood stage of malaria infection. The methods are evaluated with simulation output from a stochastic agent-based model, and are applied to an interrupted time-series study from Bongo District in northern Ghana before and immediately after a three-round transient indoor residual spraying (IRS) intervention. We incorporate into the sampling of the simulation output, limitations representative of those encountered in the collection of field data, including under-sampling of var genes, missing data, and usage of antimalarial drug treatment. We address these limitations in MOI estimates with a Bayesian framework and an imputation bootstrap approach. We demonstrate that both proposed methods give good and consistent FOI estimates across various simulated scenarios. Their application to the field surveys shows a pronounced reduction in annual FOI during intervention, of more than 70%. The proposed approach should be applicable to the many geographical locations where cohort or cross-sectional studies with regular and frequent sampling are lacking but single-time-point surveys under sparse sampling schemes are available, and for MOI estimates obtained in different ways. They should also be relevant to other pathogens of humans, wildlife and livestock whose immune evasion strategies are based on large antigenic variation resulting in high multiplicity of infection.