Stochastic lattice-based modelling of malaria dynamics

Abstract

Background

The transmission of malaria is highly variable and depends on a range of climatic and anthropogenic factors. In addition, the dispersal of Anopheles mosquitoes is a key determinant that affects the persistence and dynamics of malaria. Simple, lumped-population models of malaria prevalence have been insufficient for predicting the complex responses of malaria to environmental changes.

Methods and results

A stochastic lattice-based model that couples a mosquito dispersal and a susceptible-exposed-infected-recovered epidemics model was developed for predicting the dynamics of malaria in heterogeneous environments. The It \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{o}$$\end{document} approximation of stochastic integrals with respect to Brownian motion was used to derive a model of stochastic differential equations. The results show that stochastic equations that capture uncertainties in the life cycle of mosquitoes and interactions among vectors, parasites, and hosts provide a mechanism for the disruptions of malaria. Finally, model simulations for a case study in the rural area of Kilifi county, Kenya are presented.

Conclusions

A stochastic lattice-based integrated malaria model has been developed. The applicability of the model for capturing the climate-driven hydrologic factors and demographic variability on malaria transmission has been demonstrated.