# American Institute of Mathematical Sciences

November  2014, 19(9): 2993-3018. doi: 10.3934/dcdsb.2014.19.2993

## A reaction-diffusion model of dengue transmission

 1 School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631 2 School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

Received  July 2013 Revised  April 2014 Published  September 2014

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 $\mathcal{R}_0$. In the case of an unbounded spatial habitat, we establish the existence of the traveling wave solutions connecting the two constant steady states when $\mathcal{R}_0>1$, and the nonexistence of the traveling wave solutions that connect the disease-free steady state itself when $\mathcal{R}_0<1$. Numerical simulations are performed to illustrate the main analytic results.
Citation: Zhiting Xu, Yingying Zhao. A reaction-diffusion model of dengue transmission. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2993-3018. doi: 10.3934/dcdsb.2014.19.2993
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