Open Access
SUMMER 2014 Traveling waves for a nonlocal dispersal SIR model with standard incidence
Wan-Tong Li, Fei-Ying Yang
J. Integral Equations Applications 26(2): 243-273 (SUMMER 2014). DOI: 10.1216/JIE-2014-26-2-243


This paper is concerned with traveling wave solutions of a nonlocal dispersal SIR epidemic model with standard incidence. We show that our results on existence and nonexistence of traveling wave solutions are determined by the basic reproduction number of the corresponding ordinary differential model and the minimal wave speed. These threshold dynamics are proved by constructing an invariant cone and applying Schauder's fixed point theorem on this cone and the Laplace transform. The main difficulties are the lack of an occurrence of a regularizing effect and the loss of the order-preserving property of this model.


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Wan-Tong Li. Fei-Ying Yang. "Traveling waves for a nonlocal dispersal SIR model with standard incidence." J. Integral Equations Applications 26 (2) 243 - 273, SUMMER 2014.


Published: SUMMER 2014
First available in Project Euclid: 21 July 2014

zbMATH: 1295.35170
MathSciNet: MR3233520
Digital Object Identifier: 10.1216/JIE-2014-26-2-243

Primary: 35K57 , 35R20 , 92D25

Keywords: Laplace transform , nonlocal dispersal , Schauder's fixed point theorem , SIR model , Traveling waves

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.26 • No. 2 • SUMMER 2014
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