Journal of Mathematical Biology

, Volume 28, Issue 4, pp 451–462

Models for the spread of universally fatal diseases

  • F. Brauer

DOI: 10.1007/BF00178328

Cite this article as:
Brauer, F. J. Math. Biol. (1990) 28: 451. doi:10.1007/BF00178328


In the formulation of models of S-I-R type for the spread of communicable diseases it is necessary to distinguish between diseases with recovery with full immunity and diseases with permanent removal by death. We consider models which include nonlinear population dynamics with permanent removal. The principal result is that the stability of endemic equilibrium may depend on the population dynamics and on the distribution of infective periods; sustained oscillations are possible in some cases.

Key words

Epidemiology Stability of endemic equilibrium Distributed delays AIDS 

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • F. Brauer
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA

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