期刊
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
卷 73, 期 1, 页码 -出版社
SPRINGER INT PUBL AG
DOI: 10.1007/s00033-021-01666-9
关键词
Reaction-diffusion model; Mosquito-borne disease; Traveling wave solution; Basic reproduction ratio; Minimal wave speed
资金
- Natural Science Foundation of China [11971013]
- NSERC [RGPIN-2020-03911]
- Postgraduate Research & Practice Innovation Program of Jiangsu Province [KYCX20_0169]
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.
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(*).
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