Dynamical analysis of a reaction–diffusion mosquito-borne model in a spatially heterogeneous environment

Abstract

Abstract In this article, we formulate and perform a strict analysis of a reaction–diffusion mosquito-borne disease model with total human populations stabilizing at H(x) in a spatially heterogeneous environment. By utilizing some fundamental theories of the dynamical system, we establish the threshold-type results of the model relying on the basic reproduction number. Specifically, we explore the mutual impacts of the spatial heterogeneity and diffusion coefficients on the basic reproduction number and investigate the existence, uniqueness, and global attractivity of the nontrivial steady state by utilizing the arguments of asymptotically autonomous semiflows. For the case that all parameters are independent of space, the global attractivity of the nontrivial steady state is achieved by the Lyapunov function.