✦ LIBER ✦

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

✍ Scribed by Wei-min Liu; Simon A. Levin; Yoh Iwasa

Publisher: Springer
Year: 1986
Tongue: English
Weight: 834 KB
Volume: 23
Category: Article
ISSN: 0303-6812
DOI: 10.1007/bf00276956

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✦ Synopsis

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.

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