Traveling wave solutions in a two-group SIR epidemic model with constant recruitment

Lin Zhao, Zhi Cheng Wang, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


Host heterogeneity can be modeled by using multi-group structures in the population. In this paper we investigate the existence and nonexistence of traveling waves of a two-group SIR epidemic model with time delay and constant recruitment and show that the existence of traveling waves is determined by the basic reproduction number R0. More specifically, we prove that (i) when the basic reproduction number R0> 1 , there exists a minimal wave speed c> 0 , such that for each c≥ c the system admits a nontrivial traveling wave solution with wave speed c and for c< c there exists no nontrivial traveling wave satisfying the system; (ii) when R0≤ 1 , the system admits no nontrivial traveling waves. Finally, we present some numerical simulations to show the existence of traveling waves of the system.

Original languageEnglish (US)
Pages (from-to)1871-1915
Number of pages45
JournalJournal of Mathematical Biology
Issue number6-7
StatePublished - Dec 1 2018


  • Basic reproduction number
  • Constant recruitment
  • Time delay
  • Traveling wave solutions
  • Two-group epidemic model

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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