Traveling Wave Phenomena in a Kermack–McKendrick SIR Model

We study the existence and nonexistence of traveling waves of a general diffusive Kermack–McKendrick SIR model with standard incidence where the total population is not constant. The three classes, susceptible S , infected I and removed R , are all involved in the traveling wave solutions. We show t...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2016-03, Vol.28 (1), p.143-166
Main Authors: Wang, Haiyan, Wang, Xiang-Sheng
Format: Article
Language:English
Subjects:
Applications of Mathematics
Fixed points (mathematics)
Laplace transforms
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Schauder fixpoint theorem
Traveling waves
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Summary:We study the existence and nonexistence of traveling waves of a general diffusive Kermack–McKendrick SIR model with standard incidence where the total population is not constant. The three classes, susceptible S , infected I and removed R , are all involved in the traveling wave solutions. We show that the minimum wave speed of traveling waves for the three-dimensional non-monotonic system can be derived from its linearizaion at the initial disease-free equilibrium. The proof in this paper is based on Schauder fixed point theorem and Laplace transform. Our study provides a promising method to deal with high dimensional epidemic models.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-015-9506-2