Taiwanese Journal of Mathematics

Traveling Waves for a Spatial SIRI Epidemic Model

Zhiting Xu, Yixin Xu, and Yehui Huang

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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.

Article information

Taiwanese J. Math., Volume 23, Number 6 (2019), 1435-1460.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 92D30: Epidemiology 35K57: Reaction-diffusion equations 35C07: Traveling wave solutions

traveling wave solutions SIRI epidemic model basic reproduction number critical wave speed


Xu, Zhiting; Xu, Yixin; Huang, Yehui. Traveling Waves for a Spatial SIRI Epidemic Model. Taiwanese J. Math. 23 (2019), no. 6, 1435--1460. doi:10.11650/tjm/181205. https://projecteuclid.org/euclid.twjm/1545361214

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