Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 22, Issue 1-3, Pages 1370-1381Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2014.07.005
Keywords
Traveling wave solutions; Diffusive SIR model; Distributed delay; Schauder's fixed point theorem
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Funding
- National Natural Science Foundation of China (NSFC) [11326201, 11326202]
- Natural Science Basic Research Plan in Shaanxi Province of China [2013JQ1014]
- Fundamental Research Funds for the Central Universities [K5051370005]
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In this paper, we study the traveling waves of a diffusive SIR epidemic model with a class of nonlinear incidence rates of the form beta S(x,t) integral(h)(0) f(tau)g(I(x,t - tau))d tau. We find that the existence of traveling waves is determined by the basic reproduction number of the corresponding spatial- homogenous delay differential equations and the minimal wave speed. The existence proof is to introduce an auxiliary system and apply Schauder's fixed point theorem. The non- existence of traveling waves is obtained by two- sided Laplace transform. (C) 2014 Elsevier B. V. All rights reserved.
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