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Kermack and McKendrick revisited: The variable susceptibility model for infectious diseases

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Abstract

In this paper, we reformulate Kermack’s and McKendrick’s variable susceptibility model for infectious diseases as a nonlinear age-dependent population dynamics model, then we prove an existence and uniqueness result for the endemic steady state. Subsequently we discuss the local stability of the endemic steady state. Finally we show that Pease’s evolutionary epidemic model can be seen as a special case of the variable susceptibility model and discuss possible extensions.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguroku, 153-8914, Tokyo, Japan

    Hisashi Inaba

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  1. Hisashi Inaba
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Correspondence to Hisashi Inaba.

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This paper is dedicated to the memory of Professor YAMAGUTI Masaya (1925–1998).

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Inaba, H. Kermack and McKendrick revisited: The variable susceptibility model for infectious diseases. Japan J. Indust. Appl. Math. 18, 273–292 (2001). https://doi.org/10.1007/BF03168575

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  • DOI: https://doi.org/10.1007/BF03168575

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