Traveling Wave Phenomena in a Kermack-McKendrick SIR model
Analysis of PDEs
2014-02-18 v1 Populations and Evolution
Abstract
We study the existence and nonexistence of traveling waves of general diffusive Kermack-McKendrick SIR models with standard incidence where the total population is not constant. The three classes, susceptible , infected and removed , are all involved in the traveling wave solutions. We show that the minimum speed for the existence of traveling waves for this 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 and provides a promising method to deal with high dimensional epidemic models.
Keywords
Cite
@article{arxiv.1402.4118,
title = {Traveling Wave Phenomena in a Kermack-McKendrick SIR model},
author = {Haiyan Wang and Xiang-Sheng Wang},
journal= {arXiv preprint arXiv:1402.4118},
year = {2014}
}