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The dynamics of nematode infections of farmed ruminants

Published online by Cambridge University Press:  06 April 2009

M. G. Roberts  and
J. A. P. Heesterbeek
M. G. Roberts
Affiliation:
AgResearch, Wallaceville Animal Research Centre, P.O. Box 40063, Upper Hutt, New Zealand
J. A. P. Heesterbeek
Affiliation:
Agricultural Mathematics Group (GLW-DLO), P.O. Box 100, 6700 AC Wageningen, The Netherlands
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Summary

In this paper the dynamics and control of nematode parasites of farmed ruminants are discussed via a qualitative analysis of a differential equation model. To achieve this a quantity, ‘the basic reproduction quotient’ (Q0), whose definition coincides with previous definitions of R0 for macroparasites, but extends to models with periodic time-varying transition rates between parasite stages or management interventions, is introduced. This quantity has the usual threshold property: if Q0 is less than one the parasite population cannot maintain itself in the host population, and in the long term becomes extinct; but if Q0 is greater than one the parasite can invade the host population. An alternative quantity, R(E), that is often easier to calculate is also introduced, and shown to have the same threshold property. The use of these two quantities in analysing models for the dynamics of nematodes in complex situations is then demonstrated, with reference to the dynamics of mixed parasite species in one host; the effects of breeding host animals for resistance to parasitism; and the development of parasite strains that are resistant to chemotherapy. Five examples are discussed using parameters for the dynamics of nematode infections in sheep, and some statements on control policies are derived.

Keywords

host–parasite modelsmacroparasitesnematodesruminants
Type
Research Article
Information
Parasitology , Volume 110 , Issue 4 , May 1995 , pp. 493 - 502
Copyright
Copyright © Cambridge University Press 1995

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