Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models |
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| Authors: | Wei-min Liu Simon A Levin Yoh Iwasa |
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| Institution: | (1) Section of Ecology and Systematics, Corson Hall, Cornell University, 14853 Ithaca, NY, USA;(2) Ecosystems Research Center, Cornell University, USA;(3) Center for Applied Mathematics, Cornell University, USA;(4) Shanghai Institute of Biochemistry, Chinese Academy of Sciences, 200031 Shanghai, China;(5) Present address: Dept. of Biology, Faculty of Science, Kyushu University, 812 Fukuoka, Japan |
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| 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. |
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| Keywords: | Epidemiology nonlinear incidence rates Hopf bifurcation periodicities infectious diseases |
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