Traveling Wave Phenomena in a Kermack–McKendrick SIR Model

Haiyan Wang, Xiang Sheng Wang

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


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 languageEnglish (US)
Pages (from-to)143-166
Number of pages24
JournalJournal of Dynamics and Differential Equations
Issue number1
StatePublished - Mar 1 2016


  • Laplace transform
  • SIR model
  • Schauder fixed point theorem
  • Traveling waves

ASJC Scopus subject areas

  • Analysis


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