Global dynamics of a reaction–diffusion malaria model

Abstract

This paper is devoted to the study of a reaction–diffusion malaria model with a spatially and temporally heterogeneous structure. In the case of a bounded domain, we first establish the threshold type results for the mosquito-free system and disease-free system, and then establish the global dynamics for the model system in terms of the vector reproduction ratio Rv and the basic reproduction ratio R0. In the case of an unbound domain, we obtain the existence of the disease spreading speed and its coincidence with the minimal wave speed. At last, we use numerical simulations to verify our analytic results and investigate the influence of model parameters and spatial and temporal heterogeneity on the disease infection risk.