Abstract
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.
Original language | English (US) |
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Pages (from-to) | 143-166 |
Number of pages | 24 |
Journal | Journal of Dynamics and Differential Equations |
Volume | 28 |
Issue number | 1 |
DOIs | |
State | Published - Mar 1 2016 |
Keywords
- Laplace transform
- SIR model
- Schauder fixed point theorem
- Traveling waves
ASJC Scopus subject areas
- Analysis