## Taiwanese Journal of Mathematics

### Nonlinear Stability of Traveling Waves in a Monostable Epidemic Model with Delay

#### Abstract

This paper is concerned with the nonlinear stability of traveling waves of a delayed monostable epidemic model with quasi-monotone condition. We prove that the traveling wave front is exponentially stable by means of the weighted-energy method and the comparison principle to perturbation in some exponentially weighted $L^{\infty}$ spaces, when the difference between initial data and traveling wave front decays exponentially as $x \to -\infty$, but the initial data can be suitable large in other locations. Finally, we present two examples to support our theoretical results.

#### Article information

Source
Taiwanese J. Math., Volume 21, Number 6 (2017), 1381-1411.

Dates
Revised: 19 March 2017
Accepted: 27 March 2017
First available in Project Euclid: 17 August 2017

https://projecteuclid.org/euclid.twjm/1502935243

Digital Object Identifier
doi:10.11650/tjm/8048

Mathematical Reviews number (MathSciNet)
MR3732911

Zentralblatt MATH identifier
06871374

#### Citation

Wu, Xin; Ma, Zhaohai; Yuan, Rong. Nonlinear Stability of Traveling Waves in a Monostable Epidemic Model with Delay. Taiwanese J. Math. 21 (2017), no. 6, 1381--1411. doi:10.11650/tjm/8048. https://projecteuclid.org/euclid.twjm/1502935243

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