Journal of Mathematical Biology

, Volume 27, Issue 2, pp 179–190

A competitive exclusion principle for pathogen virulence

  • H. J. Bremermann
  • H. R. Thieme

DOI: 10.1007/BF00276102

Cite this article as:
Bremermann, H.J. & Thieme, H.R. J. Math. Biology (1989) 27: 179. doi:10.1007/BF00276102


For a modified Anderson and May model of host parasite dynamics it is shown that infections of different levels of virulence die out asymptotically except those that optimize the basic reproductive rate of the causative parasite. The result holds under the assumption that infection with one strain of parasite precludes additional infections with other strains. Technically, the model includes an environmental carrying capacity for the host. A threshold condition is derived which decides whether or not the parasites persist in the host population.

Key words

Co-evolution Commensalism Evolution of virulence Myxomatosis Extinction Persistence Multi-strain epidemic model Stable endemic equilibrium 

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • H. J. Bremermann
    • 1
  • H. R. Thieme
    • 2
  1. 1.Department of Biophysics and Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of MathematicsArizona State UniversityTempeUSA

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