Dynamical behavior of epidemiological models with nonlinear incidence rates

Wei min Liu, Herbert W. Hethcote, Simon A. Levin

Research output: Contribution to journalArticlepeer-review

632 Scopus citations


Epidemiological models with nonlinear incidence rates λIpSqshow a much wider range of dynamical behaviors than do those with bilinear incidence rates λIS. These behaviors are determined mainly by p and λ, and secondarily by q. For such models, there may exist multiple attractive basins in phase space; thus whether or not the disease will eventually die out may depend not only upon the parameters, but also upon the initial conditions. In some cases, periodic solutions may appear by Hopf bifurcation at critical parameter values.

Original languageEnglish (US)
Pages (from-to)359-380
Number of pages22
JournalJournal of mathematical biology
Issue number4
StatePublished - Sep 1987
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Epidemiological models
  • Homoclinic-loop bifurcation
  • Hopf bifurcation
  • Nonlinear incidence rates


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