On a vector-host epidemic model with spatial structure

In this paper, we study a reaction-diffusion vector-host epidemic model. We define the basic reproduction number R-0 and show that R-0 is a threshold parameter: if R-0 <= 1 the disease free equilibrium is globally stable; if R-0 > 1 the model has a unique globally stable positive equilibrium. Our proof combines arguments from monotone dynamical system theory, persistence theory, and the theory of asymptotically autonomous semiflows.