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

Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Biology Springer Journals

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

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References (22)

Publisher
Springer Journals
Copyright
Copyright © 1986 by Springer-Verlag
Subject
Mathematics; Mathematical and Computational Biology; Applications of Mathematics
ISSN
0303-6812
eISSN
1432-1416
DOI
10.1007/BF00276956
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Mathematical BiologySpringer Journals

Published: Aug 12, 2004

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