Taiwanese Journal of Mathematics

Traveling Wave Solutions of a Diffusive SEIR Epidemic Model with Nonlinear Incidence Rate

Lin Zhao, Liang Zhang, and Haifeng Huo

Full-text: Open access

Abstract

This paper is concerned with the existence and nonexistence of traveling wave solutions of a diffusive SEIR epidemic model with nonlinear incidence rate, which are determined by the basic reproduction number $R_0$ and the minimal wave speed $c^*$. Namely, the system admits a nontrivial traveling wave solution if $R_0 \gt 1$ and $c \geq c^*$ and then the non-existence of traveling wave solutions of the system is established if $R_0 \gt 1$ and $0 \lt c \lt c^*$. Especially, using numerical simulation, we give the basic framework of traveling wave solutions of the system.

Article information

Source
Taiwanese J. Math., Volume 23, Number 4 (2019), 951-980.

Dates
Received: 5 May 2018
Revised: 20 October 2018
Accepted: 24 October 2018
First available in Project Euclid: 18 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1563436876

Digital Object Identifier
doi:10.11650/tjm/181009

Mathematical Reviews number (MathSciNet)
MR3982069

Zentralblatt MATH identifier
07088955

Subjects
Primary: 35C07: Traveling wave solutions 35B40: Asymptotic behavior of solutions 35K57: Reaction-diffusion equations 92D30: Epidemiology

Keywords
SEIR epidemic model nonlinear incidence rate the basic reproduction number the minimal speed traveling wave solutions

Citation

Zhao, Lin; Zhang, Liang; Huo, Haifeng. Traveling Wave Solutions of a Diffusive SEIR Epidemic Model with Nonlinear Incidence Rate. Taiwanese J. Math. 23 (2019), no. 4, 951--980. doi:10.11650/tjm/181009. https://projecteuclid.org/euclid.twjm/1563436876


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