Journal of Mathematical Biology

, Volume 30, Issue 7, pp 717–731

Disease transmission models with density-dependent demographics

  • Linda Q. Gao
  • Herbert W. Hethcote

DOI: 10.1007/BF00173265

Cite this article as:
Gao, L.Q. & Hethcote, H.W. J. Math. Biol. (1992) 30: 717. doi:10.1007/BF00173265


The models considered for the spread of an infectious disease in a population are of SIRS or SIS type with a standard incidence expression. The varying population size is described by a modification of the logistic differential equation which includes a term for disease-related deaths. The models have density-dependent restricted growth due to a decreasing birth rate and an increasing death rate as the population size increases towards its carrying capacity. Thresholds, equilibria and stability are determined for the systems of ordinary differential equations for each model. The persistence of the infectious disease and disease-related deaths can lead to a new equilibrium population size below the carrying capacity and can even cause the population to become extinct.

Key words

Epidemiological modelDensity-dependent logistic growthThresholdsStability

Copyright information

© Springer-Veriag 1992

Authors and Affiliations

  • Linda Q. Gao
    • 1
  • Herbert W. Hethcote
    • 1
  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA