Traveling wave solutions in a two-group epidemic model with latent period

Lin Zhao, Zhi Cheng Wang, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


In this paper, we propose a susceptible-infective-recovered (SIR) epidemic model to describe the geographic spread of an infectious disease in two groups/sub-populations living in a spatially continuous habitat. It is assumed that the susceptibility of individuals for infection and the infectivity of individuals are distinct between these two groups/sub-populations. It is also assumed that the infectious disease has a fixed latent period and the latent individuals may diffuse. We investigate the traveling wave solutions and obtain complete information about the existence and nonexistence of nontrivial traveling wave solutions. We prove that when the basic reproduction number at the disease free equilibrium , there exists a critical number c > 0 such that for each c > c , the system admits a nontrivial traveling wave solution with wave speed c, and for c < c , the system admits no nontrivial traveling wave solution. When , we show that there exists no nontrivial traveling wave solution. In addition, for the case and c > c , we also find that the final sizes of susceptible individuals, denoted by , satisfies , which means that there is no outbreak of this the infectious disease anymore. At last, we analyze and simulate the continuous dependence of the minimal speed c on the parameters.

Original languageEnglish (US)
Pages (from-to)1287-1325
Number of pages39
Issue number4
StatePublished - Feb 14 2017


  • 35B40
  • 35K57
  • 35R10
  • 92D30
  • different infectivity
  • different susceptibility
  • epidemic model
  • latent period Mathematics Subject Classification numbers: 35C07
  • traveling wave solutions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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