Patterns in the effects of infectious diseases on population growth

O. Diekmann*, M. Kretzschmar

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

An infectious disease may reduce or even stop the exponential growth of a population. We consider two very simple models for microparasitic and macroparasitic diseases, respectively, and study how the effect depends on a contact parameter K. The results are presented as bifurcation diagrams involving several threshold values of к. The precise form of the bifurcation diagram depends critically on a second parameter ζ, measuring the influence of the disease on the fertility of the hosts. A striking outcome of the analysis is that for certain ranges of parameter values bistable behaviour occurs: either the population grows exponentially or it oscillates periodically with large amplitude.

Original languageEnglish
Pages (from-to)539-570
Number of pages32
JournalJournal of Mathematical Biology
Volume29
Issue number6
DOIs
Publication statusPublished - 1 Jan 1991

Keywords

  • Bistable behaviour
  • Epidemic
  • Oscillations
  • Population regulation
  • Threshold values for contact parameter

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