English

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 SS, infected II and removed RR, 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}
}