一类具有时滞的反应扩散登革热传染病模型的行波解

摘要/Abstract

摘要：

该文研究了一类时滞反应扩散登革热传染病模型行波解的存在性与不存在性. 首先, 利用辅助系统并结合Schauder不动点定理, 证明了当基本再生数${\cal R}_0>1$, $c>c_\ast$时, 系统存在单调有界正行波解. 其次, 当${\cal R}_0>1$, $0<c<c_\ast$时, 借助双边Laplace变换, 得到行波的不存在性；运用比较原理和反证法, 证明了当${\cal R}_0\leq1$, $c>0$时行波的不存在性. 最后, 从理论和数值方面探讨了潜伏期和扩散率对阈值速度$c_\ast$的影响. 结论表明：适当延长潜伏期或减少个体扩散可降低疾病传播速度.

关键词: 行波解, 登革热, 时滞, 基本再生数, 阈值速度

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

中图分类号:

王凯,赵洪涌. 一类具有时滞的反应扩散登革热传染病模型的行波解[J]. 数学物理学报, 2022, 42(4): 1209-1226.

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.

图/表 3

参考文献 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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