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December, 2019 Traveling Waves for a Spatial SIRI Epidemic Model
Zhiting Xu, Yixin Xu, Yehui Huang
Taiwanese J. Math. 23(6): 1435-1460 (December, 2019). DOI: 10.11650/tjm/181205

Abstract

The aim of this paper is to study the traveling waves in a spatial SIRI epidemic model arising from herpes viral infection. We obtain the complete information about the existence and non-existence of traveling waves in the model. Namely, we prove that when the basic reproduction number $\mathcal{R}_0 \gt 1$, there exists a critical wave speed $c^* \gt 0$ such that for each $c \gt c^*$, the model admits positive traveling waves; and for $c \lt c^*$, the model has no non-negative and bounded traveling wave. We also give some numerical simulations to illustrate our analytic results.

Citation

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Zhiting Xu. Yixin Xu. Yehui Huang. "Traveling Waves for a Spatial SIRI Epidemic Model." Taiwanese J. Math. 23 (6) 1435 - 1460, December, 2019. https://doi.org/10.11650/tjm/181205

Information

Received: 23 June 2018; Revised: 30 November 2018; Accepted: 10 December 2018; Published: December, 2019
First available in Project Euclid: 21 December 2018

zbMATH: 07142981
MathSciNet: MR4033553
Digital Object Identifier: 10.11650/tjm/181205

Subjects:
Primary: 35C07 , 35K57 , 92D30

Keywords: Basic reproduction number , critical wave speed , SIRI epidemic model , traveling wave solutions

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 6 • December, 2019
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