Traveling waves in a nonlocal dispersal epidemic model with spatio-temporal delay

Jingdong Wei; Jiangbo Zhou; Wenxia Chen; Zaili Zhen; Lixin Tian

doi:10.3934/cpaa.2020125

Article Contents

2020, Volume 19, Issue 5: 2853-2886. Doi: 10.3934/cpaa.2020125

This issue Previous Article Nonexistence results on the space or the half space of

$ -\Delta u+\lambda u = |u|^{p-1}u $

via the Morse index Next Article Existence of ground state solution and concentration of maxima for a class of indefinite variational problems

Traveling waves in a nonlocal dispersal epidemic model with spatio-temporal delay

1.
Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
2.
School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210046, China

^*Corresponding author
^*Corresponding author

Received: June 2019

Revised: November 2019

Published: March 2020

This research was supported by National Natural Science Foundation of China (No. 11731014) and China Postdoctoral Science Foundation (No. 2018M642173)

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Abstract

In this paper, we investigate the existence and nonexistence of traveling wave solutions in a nonlocal dispersal epidemic model with spatio-temporal delay. It is shown that this model admits a nontrivial positive traveling wave solution when the basic reproduction number $ R_0>1 $ and the wave speed $ c\geq c^* $ ($ c^* $ is the critical speed) and this model has no traveling wave solutions when $ R_0\leq1 $ or $ c<c^* $. This indicates that $ c^* $ is the minimal wave speed.

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Mathematics Subject Classification: Primary: 35K55, 35C07, 92D30, 92B05, 35B40.

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Figure 1. $ I_+^*(z) $ and $ I_-^*(z) $

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