Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
type: Item
instance of: scholarly article
title: Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
zbMATH Open document ID: 0582.92023
DOI: 10.1007/BF00276956
author: Wei-min Liu
author: Simon Levin
author: Yoh Iwasa
published in: Journal of Mathematical Biology
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 3932852
zbMATH Keywords: epidemiology
zbMATH Keywords: periodicities
zbMATH Keywords: infectious diseases
zbMATH Keywords: SIRS model
zbMATH Keywords: Hopf bifurcations
zbMATH Keywords: saddle-node bifurcations
zbMATH Keywords: homoclinic loop bifurcations
zbMATH Keywords: nonlinear incidence rates
Wikidata QID: Q52649546
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3932852