Dynamical behavior of epidemiological models with nonlinear incidence rates

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

Research output: Contribution to journalArticle

478 Scopus citations

Abstract

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
Volume25
Issue number4
DOIs
StatePublished - Sep 1 1987
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

Keywords

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

Fingerprint Dive into the research topics of 'Dynamical behavior of epidemiological models with nonlinear incidence rates'. Together they form a unique fingerprint.

  • Cite this