Journal of Mathematical Biology

, Volume 33, Issue 4, pp 415–434

Threshold quantities for helminth infections

  • J. A. P. Heesterbeek
  • M. G. Roberts

DOI: 10.1007/BF00176380

Cite this article as:
Heesterbeek, J.A.P. & Roberts, M.G. J. Math. Biol. (1995) 33: 415. doi:10.1007/BF00176380


For parasites with a clearly defined life-cycle we give threshold quantities that determine the stability of the parasite-free steady state for autonomous and periodic deterministic systems formulated in terms of mean parasite burdens. We discuss the biological interpretations of the quantities, how to deal with heterogeneity in both parasite and host populations, how to incorporate the effects of periodic discontinuities, and the relation of the threshold quantities to the basic reproduction ratio R0. Examples from the literature are given. The analysis of the periodic case extends easily to ‘micro-parasitic’ systems.

Key words

Deterministic epidemic modelsHelminths(Non) autonomous systemsThreshold behaviourBasic reproduction ratioHeterogeneity

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • J. A. P. Heesterbeek
    • 1
  • M. G. Roberts
    • 2
  1. 1.Department of ZoologyUniversity of OxfordOxfordUK
  2. 2.AgResearch, Wallaceville Animal Research CentreUpper HuttNew Zealand
  3. 3.Agricultural Mathematics Group (GLW-DLO)WageningenThe Netherlands