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Population size dependent incidence in models for diseases without immunity

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Abstract

Epidemiological models of SIS type are analyzed to determine the thresholds, equilibria, and stability. The incidence term in these models has a contact rate which depends on the total population size. The demographic structures considered are recruitment-death, generalized logistic, decay and growth. The persistence of the disease combined with disease-related deaths and reduced reproduction of infectives can greatly affect the population dynamics. For example, it can cause the population size to decrease to zero or to a new size below its carrying capacity or it can decrease the exponential growth rate constant of the population.

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  1. Department of Mathematics, University of Iowa, 52242, Iowa City, Iowa, USA

    Jinshi Zhou & Herbert W. Hethcote

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  1. Jinshi Zhou
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Zhou, J., Hethcote, H.W. Population size dependent incidence in models for diseases without immunity. J. Math. Biol. 32, 809–834 (1994). https://doi.org/10.1007/BF00168799

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