Threshold Kinetic Analysis Of A Class Of Mosquito-borne Infectious Disease Models With Spatial Heterogeneity

Taking malaria infectious disease transmission as the main background,In this paper we formulate a reaction-diffusion mosquito-borne disease model with susceptible humans stabilizing at H(x)in a spatially heterogeneous environment.the model is more complex and enriches the research content of malaria infectious disease transmission.We analyze the well-posedness of the model,define the basic reproduction number,and study explore the impacts of the small and large diffusion coefficients and spatial heterogeneity on the basic reproduction number.Moreover,we discuss the threshold dynamics in terms of the basic reproduction number by comparison principle and the principal eigenvalue of the as sociated eigenvalue problem.Specifically,we investigate the existence and uniqueness of the nontrivial steady state corresponding to a positive steady state and obtain the global attractivity of the positive steady state by using the theory of asymptotically autonomous semiflows.In a homogeneous case,we verify the global attractivity of the positive constant steady state by the technique of Lyapunov function.