一类具有时滞的反应扩散登革热传染病模型的行波解

Abstract

Abstract:

In this paper, we investigate the existence and nonexistence of traveling wave solution (TWS) for a reaction-diffusion dengue epidemic model with time delays. Firstly, by introducing an auxiliary system and combining with Schauder's fixed-point theorem, it is proved that when the basic reproduction number ${\cal R}_0>1$, $c>c_\ast$, the system admits a positive bounded monotone TWS. Secondly, when ${\cal R}_0>1$, $0<c<c_\ast$, by means of two-sided Laplace transform, the nonexistence of TWS is obtained. When ${\cal R}_0\leq1$, there is no TWS for any wave speed $c>0$ with the aid of comparison principle and contradictory arguments. Lastly, the effects of incubation period and individual diffusion on the threshold speed $c_\ast$ are studied theoretically and numerically. The conclusion shows that prolonging the length of incubation period or decreasing the individual diffusion will reduce the speed of disease transmission.

Key words: Traveling wave solution, Dengue, Delay, Basic reproduction number, Threshold speed

CLC Number:

Kai Wang,Hongyong Zhao. Traveling Wave of a Reaction-Diffusion Dengue Epidemic Model with Time Delays[J].Acta mathematica scientia,Series A, 2022, 42(4): 1209-1226.

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References 29

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参数	含义
$d_i$	人和蚊子的扩散系数($i=1, 2, 3, 4$)
$\mu_h$	染病者的因病死亡率
$\mu_v$	染病蚊子的因病死亡率
$\alpha_h$	染病者的恢复率
$k_{1}(k_{2})$	病毒由染病蚊子(人)到易感人(蚊子)的传播率

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Traveling Wave of a Reaction-Diffusion Dengue Epidemic Model with Time Delays

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