Traveling waves for a diffusive mosquito-borne epidemic model with general incidence

In this paper, we obtain the complete information about the existence and nonexistence of traveling wave solution (TWS) for a reaction-diffusion model of mosquito-borne disease with general incidence and constant recruitment. We find that the basic reproduction ratio No of the corresponding kinetic system and the minimal wave speed c(*) are thresholds to determine the existence of TWS. With the aid of limiting arguments and Lyapunov approach, it is demonstrated that the system possesses a nontrivial TWS with wave speed c >= c(*) connecting the disease-free equilibrium and endemic equilibrium when R-0 > 1. When R-0 <= 1 and c > 0, the nonexistence of nontrivial TWS is obtained by contradiction. By means of a rather ingenious method that is easier to understand than Laplace transform, we show that there is no nontrivial TWS when R-0 > 1 and 0 < c < c(*). Numerically, we perform simulations to verify the analytical results and explore the sensitivity of the speed c(*) on parameters. The sensitivity results show that the parameters related to mosquitoes have a greater impact on c(*).

Automated summary

This paper investigates the existence and nonexistence of traveling wave solutions for a reaction-diffusion model of mosquito-borne disease. The results are verified numerically, and the sensitivity of the wave speed is explored.