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., Advance publication (2019), 26 pages.

First available in Project Euclid: 21 December 2018

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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., advance publication, 21 December 2018. doi:10.11650/tjm/181205. https://projecteuclid.org/euclid.twjm/1545361214

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