From multiplicity of infection to force of infection for sparsely sampled 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. This high MOI accompanies high asymptomatic 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 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 from MOI, in the form of either a two-moment approximation method or Little's Law. We illustrate these two methods with MOI estimates obtained under sparse sampling schemes with the " coding" approach. The two methods use infection duration data from naive malaria therapy patients with neurosyphilis. Consequently, they are suitable for FOI inference in subpopulations with a similar immune profile and the highest vulnerability, for example, infants or toddlers. Both 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. The sampling of the simulation output incorporates limitations representative of those encountered in the collection of field data, including under-sampling of genes, missing data, and antimalarial drug treatment. We address these limitations in MOI estimates with a Bayesian framework and an imputation bootstrap approach. Both methods yield good and replicable FOI estimates across various simulated scenarios. Applying these methods to the subpopulation of children aged 1-5 years in Ghana field surveys shows over a 70% reduction in annual FOI immediately post-intervention. The proposed methods should be applicable to geographical locations lacking cohort or cross-sectional studies with regular and frequent sampling but having single-time-point surveys under sparse sampling schemes, and for MOI estimates obtained in different ways. They should also be relevant to other pathogens whose immune evasion strategies are based on large antigenic variation resulting in high MOI.