Time Periodic Traveling Waves for a Periodic and Diffusive SIR Epidemic Model

In this paper, we study the time periodic traveling wave solutions for a periodic SIR epidemic model with diffusion and standard incidence. We establish the existence of periodic traveling waves by investigating the fixed points of a nonlinear operator defined on an appropriate set of periodic funct...

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Bibliographic Details
Published inJournal of dynamics and differential equations Vol. 30; no. 1; pp. 379 - 403
Main Authors Wang, Zhi-Cheng, Zhang, Liang, Zhao, Xiao-Qiang
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2018
Springer Nature B.V
Subjects
Applications of Mathematics
Epidemics
Fixed points (mathematics)
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Periodic functions
Traveling waves
Diffusive SIR model
Periodic traveling waves
92D30
Schauder fixed point theorem
Time
35B40
35K57
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Summary:In this paper, we study the time periodic traveling wave solutions for a periodic SIR epidemic model with diffusion and standard incidence. We establish the existence of periodic traveling waves by investigating the fixed points of a nonlinear operator defined on an appropriate set of periodic functions. Then we prove the nonexistence of periodic traveling via the comparison arguments combined with the properties of the spreading speed of an associated subsystem.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-016-9546-2