Journal of Mathematical Biology

, Volume 32, Issue 8, pp 809–834

Population size dependent incidence in models for diseases without immunity

  • Jinshi Zhou
  • Herbert W. Hethcote

DOI: 10.1007/BF00168799

Cite this article as:
Zhou, J. & Hethcote, H.W. J. Math. Biol. (1994) 32: 809. doi:10.1007/BF00168799


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 

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Jinshi Zhou
    • 1
  • Herbert W. Hethcote
    • 1
  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA

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