Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models

Wei min Liu, Simon A. Levin, Yoh Iwasa

Research output: Contribution to journalArticlepeer-review

506 Citations (Scopus)

Abstract

When the traditional assumption that the incidence rate is proportional to the product of the numbers of infectives and susceptibles is dropped, the SIRS model can exhibit qualitatively different dynamical behaviors, including Hopf bifurcations, saddle-node bifurcations, and homoclinic loop bifurcations. These may be important epidemiologically in that they demonstrate the possibility of infection outbreak and collapse, or autonomous periodic coexistence of disease and host. The possible mechanisms leading to nonlinear incidence rates are discussed. Finally, a modified general criterion for supercritical or subcritical Hopf bifurcation of 2-dimensional systems is presented.

Original languageEnglish
Pages (from-to)187-204
Number of pages18
JournalJournal of Mathematical Biology
Volume23
Issue number2
DOIs
Publication statusPublished - Feb 1986
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)
  • Agricultural and Biological Sciences (miscellaneous)

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