Threshold dynamics of a malaria transmission model in periodic environment

Abstract

In this paper, we propose a malaria transmission model with periodic environment. The basic reproduction number R0 is computed for the model and it is shown that the disease-free periodic solution of the model is globally asymptotically stable when R0<1, that is, the disease goes extinct when R0<1, while the disease is uniformly persistent and there is at least one positive periodic solution when R0>1. It indicates that R0 is the threshold value determining the extinction and the uniform persistence of the disease. Finally, some examples are given to illustrate the main theoretical results. The numerical simulations show that, when the disease is uniformly persistent, different dynamic behaviors may be found in this model, such as the global attractivity and the chaotic attractor.