The epidemiology of Plasmodium falciparum malaria presents a unique set of challenges due to the complicated dynamics of infection, immunity, disease, and detection. Studies of malaria epidemiology commonly measure malaria parasite densities or prevalence, but since malaria is so complex with so many factors to consider, a complete mathematical synthesis of malaria epidemiology has been elusive. Here, we take a new approach. From a simple model of malaria exposure and infection in human cohorts as they age, we develop random variables describing the multiplicity of infection (MoI) and the age of infection (AoI). Next, using the MoI and AoI distributions, we develop random variables describing parasite densities, parasite counts, and detection. We also derived a random variable describing the age of the youngest infection (AoY), which can be used to compute approximate parasite densities in complex infections. Finally, we derive a simple system of differential equations with hybrid variables that track the mean MoI, AoI and AoY, and we show it matches the complex probabilistic system with reasonable accuracy. We can thus compute the state of any individual chosen at random from the population in two ways. The same approach – pairing random variables and hybrid models – can be extended to model other features of malaria epidemiology, including disease, malaria immunity, treatment and chemoprotection, and infectiousness. The computational simplicity of hybrid models has some advantages over compartmental models and stochastic individual-based models, and with the supporting probabilistic framework, provide a sound basis for a synthesis of observational malaria epidemiology.

Significance The probabilistic framework presented here represents a step forward in the theory for observational malaria epidemiology. Using these methods, one can connect the heterogeneous dynamics of individual infections to both observational and process uncertainty in estimates of population-level metrics such as cross-sectional surveys of prevalence by light microscopy. This serves as a basis for more complex simulation studies using the present models and extensions that include factors such as fever, treatment, and transmission.

The authors have declared no competing interest.

This research was supported by a grant from the National Institute of Allergies and Infectious Diseases (R01 AI163398), which supported DLS, JMH, and ARC. Additional support for DLS from the Bill and Melinda Gates Foundation (INV 030600).

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https://doi.org/10.1017/S0031182001007533

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