Weather-driven malaria transmission model with gonotrophic and sporogonic cycles

Abstract

Malaria is mainly a tropical disease and its transmission cycle is heavily influenced by environment: The life-cycles of the Anopheles mosquito vector and Plasmodium parasite are both strongly affected by ambient temperature, while suitable aquatic habitat is necessary for immature mosquito development. Therefore, how global warming may affect malaria burden is an active question, and we develop a new ordinary differential equations-based malaria transmission model that explicitly considers the temperature-dependent Anopheles gonotrophic and Plasmodium sporogonic cycles. Mosquito dynamics are coupled to infection among a human population with symptomatic and asymptomatic disease carriers, as well as temporary immunity. We also explore the effect of incorporating diurnal temperature variations upon transmission. Rigorous analysis of the model show that the non-trivial disease-free equilibrium is locallyasymptotically stable when the associated reproduction number is less than unity (this equilibrium is globally-asymptotically for a special case with no density-dependent larval and disease-induced host mortality). Numerical simulations of the model, for the case where the ambient temperature is held constant, suggest a nonlinear, hyperbolic relationship between the reproduction number and clinical malaria burden. Moreover, malaria burden peaks at 29.5 oC when daily ambient temperature is held constant, but this peak decreases with increasing daily temperature variation, to about 23–25 oC. Malaria burden also varies nonlinearly with temperature, such that small temperature changes influent disease mainly at marginal temperatures, suggesting that in areas where malaria is highly endemic, any response to global warming may be highly nonlinear and most typically minimal, while in areas of more marginal malaria potential (such as the East African highlands), increasing temperatures may translate nearly linearly into increased disease potential. Finally, we observe that while explicitly modelling the stages of the Plasmodium sporogonic cycle is essential, explicitly including the stages of the Anopheles gonotrophic cycle is of minimal importance.