Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (4): 1209-1226.

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

Kai Wang(),Hongyong Zhao*()   

  1. Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106
  • Received:2021-01-27 Online:2022-08-26 Published:2022-08-08
  • Contact: Hongyong Zhao E-mail:kwang@nuaa.edu.cn;hyzho1967@126.com
  • Supported by:
    the NSFC(11971013);the NSFC(12101309);Postgraduate Research & Practice Innovation Program of Jiangsu Province(KYCX20_0169);the China Postdoctoral Science Foundation(2021M691577)

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: 

  • O29
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