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Traveling wave solutions for a delayed diffusive SIR epidemic model with nonlinear incidence rate and external supplies
Author(s) -
Zhou Kai,
Han Maoan,
Wang Qiru
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4197
Subject(s) - traveling wave , epidemic model , laplace transform , mathematics , nonlinear system , schauder fixed point theorem , constant (computer programming) , mathematical analysis , fixed point theorem , wave speed , lyapunov function , physics , picard–lindelöf theorem , demography , population , quantum mechanics , sociology , computer science , programming language
In this paper, we study the traveling wave solutions of a delayed diffusive SIR epidemic model with nonlinear incidence rate and constant external supplies. We find that the existence of traveling wave solutions is determined by the basic reproduction number of the corresponding spatial‐homogenous delay differential system and the minimal wave speed. The existence is proved by applying Schauder's fixed point theorem and Lyapunov functional method. The non‐existence of traveling waves is obtained by two‐sided Laplace transform. Copyright © 2016 John Wiley & Sons, Ltd.