Journal of Mathematical Biology

, Volume 32, Issue 8, pp 809-834

First online:

Population size dependent incidence in models for diseases without immunity

  • Jinshi ZhouAffiliated withDepartment of Mathematics, University of Iowa
  • , Herbert W. HethcoteAffiliated withDepartment of Mathematics, University of Iowa

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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.

Key words

Epidemiological modeling SIS Models Density-dependent incidence Thresholds Logistic growth