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. 1986;23(2):187-204.
doi: 10.1007/BF00276956.

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

W M Liu, S A Levin, Y Iwasa

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

W M Liu et al. J Math Biol. 1986.

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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References

    1. Am J Epidemiol. 1973 Dec;98(6):469-82 - PubMed
    1. Proc Natl Acad Sci U S A. 1945 Apr;31(4):109-16 - PubMed
    1. IMA J Math Appl Med Biol. 1984;1(2):169-91 - PubMed
    1. Proc Natl Acad Sci U S A. 1945 Jan;31(1):24-34 - PubMed
    1. J Theor Biol. 1984 Oct 21;110(4):665-79 - PubMed

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