Global Dynamics of a Reaction-diffusion Malaria Model with Seasonality
Malaria is an infectious disease caused by the Plasmodium parasite and it is trans-mitted among humans through bites of adult female Anopheles mosquitoes.To investigate the effects of spatial heterogeneities and seasonality,we develop a periodic reaction-diffusion model.Since the total density of mosquitoes tends to be a positive periodic solution,we are focus on the limiting system associated with the original system.We first introduce the basic reproduction number R0 and then show that R0 serves as a threshold parameter in determining the global dynamics of the limiting system by employing the theory of monotone and subhomogeneous systems.More precisely,the disease-free periodic solution is globally asymptotically stable if R0≤ 1,and the model admits a unique positive periodic solution that is globally asymptoti-cally stable when R0＞1.Finally,the threshold type result for the limiting system is lifted to the original system with the help of the theory of chain transitive sets.
NETL
NSTL
万方数据
