A reaction-diffusion model of dengue transmission

Abstract

This paper is devoted to the mathematical analysis of a reaction-diffusion model of dengue transmission. In the case of a bounded spatial habitat, we obtain the local stability as well as the global stability of either disease-free or endemic steady state in terms of the basic reproduction number R0. In the case of an unbounded spatial habitat, we establish the existence of the traveling wave solutions connecting the two constant steady states when R0> 1, and the nonexistence of the traveling wave solutions that connect the disease-free steady state itself when R0< 1. Numerical simulations are performed to illustrate the main analytic results.