Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-26T04:45:48.636Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anderson, R. M. (1982). The Population Dynamics of Infectious Diseases: Theory and Applications. New York: Chapman & Hall.Google Scholar
Anderson, R. M. & May, R. M. (1982). The Population Biology of Infectious Diseases. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Anderson, R. M. & May, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press.CrossRefGoogle Scholar
Anderson, R. M., May, R. M. & Gupta, S. (1989). Nonlinear phenomena in host–parasite interactions. Parasitology 99, S59–S79.CrossRefGoogle ScholarPubMed
Barnes, E. H. & Dobson, R. J. (1990). Population dynamics of Trichostrongylus colubriformis in sheep: a computer model to simulate grazing systems and the evolution of anthelmintic resistance. International Journal for Parasitology 20, 823–31.CrossRefGoogle ScholarPubMed
Diekmann, O., Heesterbeek, J. A. P. & Metz, J. A. J. (1990). The definition and computation of the basic reproduction ratio R 0 in models of infectious diseases in heterogeneous populations. Journal of Mathematical Biology 28, 365–82.CrossRefGoogle ScholarPubMed
Diekmann, O., Heesterbeek, J. A. P. & Metz, J. A. J. (1994). The legacy of Kermack and McKendrick. In Epidemic Models, their Structure and Relation to Data (ed. Mollison, D.) Cambridge: Cambridge University Press (In the Press.)Google Scholar
Dobson, A. P. (1985). The population dynamics of competition between parasites. Parasitology 91, 317–47.CrossRefGoogle ScholarPubMed
Dobson, A. P. & Grenfell, B. T. (1994). Ecology of Infectious Diseases in Natural Populations. Cambridge: Cambridge University Press (In the Press.)Google Scholar
Dobson, R. J., Barnes, E. H. & Windon, R. G. (1992). Population dynamics of Trichostrongylus colubriformis and Ostertagia circumcincta in single and concurrent infections. International Journal for Parasitology 22, 997–1004.CrossRefGoogle ScholarPubMed
Grenfell, B. T., Smith, G. & Anderson, R. M. (1987). A mathematical model of the population biology of Ostertagia ostertagi in calves and yearlings. Parasitology 95, 389–406.CrossRefGoogle ScholarPubMed
Heesterbeek, J. A. P. (1992). R 0. Ph.D. thesis. University of Leiden.Google Scholar
Heesterbeek, J. A. P. & Roberts, M. G. (1994). Threshold properties for helminth infections. Journal of Mathematical Biology (In the Press.)Google Scholar
Kermack, W. O. & McKendrick, A. G. (1927). Contributions to the mathematical theory of epidemics – 1. Proceedings of the Royal Society 115A, 700–21. Reprinted as Bulletin of Mathematical Biology 53, 33–55 (1991).Google Scholar
Leathwick, D. M., Barlow, N. D. & Vlassoff, A. (1992). A model for nematodiasis in New Zealand lambs. International Journal for Parasitology 22, 789–99.CrossRefGoogle Scholar
Mollison, D. (1994). Epidemic Models, their Structure and Relation to Data. Cambridge: Cambridge University Press (In the Press.)Google Scholar
Mollison, D., Isham, V. & Grenfell, B. T. (1994). Epidemics: models and data. Journal of the Royal Statistical Society A 157, 115–49.CrossRefGoogle ScholarPubMed
Roberts, M. G. (1994 a). Discussion section of Mollison, Isham & Grenfell (1994), p. 136. Epidemics: models and data. Journal of the Royal Statistical Society A 157, 115–49.Google Scholar
Roberts, M. G. (1994 b). The population dynamics of nematode infections of ruminants. In Proceedings of the Third International Conference on Mathematical Population Dynamics, University of Pau, 1–5 June 1992, (ed. Kimmel, M.), Winnipeg: Wuerz Publishing (In the Press.)Google Scholar
Roberts, M. G. & Dobson, A. P. (1994). The population dynamics of communities of parasitic helminths. Mathematical Biosciences (in the Press.)Google Scholar
Roberts, M. G. & Grenfell, B. T. (1991). The population dynamics of nematode infections of ruminants: periodic perturbations as a model for management. IMA Journal of Mathematics Applied in Medicine and Biology 8, 83–93.CrossRefGoogle Scholar
Roberts, M. G. & Grenfell, B. T. (1992). The population dynamics of nematode infections of ruminants: the effect of seasonality in the free-living stages. IMA Journal of Mathematics Applied in Medicine and Biology 9, 29–41.CrossRefGoogle ScholarPubMed
Roberts, M. G., Lawson, J. R. & Gemmell, M. A. (1987). Population dynamics in echinococcosis and cysticercosis: Mathematical model of the life-cycles of Taenia hydatigena and T. ovis. Parasitology 94, 181–97.CrossRefGoogle ScholarPubMed
Roberts, M. G., Smith, G. & Grenfell, B. T. (1994). Mathematical models for macroparasites of wildlife. In Ecology of Infectious Diseases in Natural Populations, (ed. Dobson, A. P. & Grenfell, B. T.), Cambridge: Cambridge University Press (In the Press.)Google Scholar
Scott, M. E. & Smith, G. (1994). Parasitic and Infectious Diseases: Epidemiology and Ecology. San Diego: Academic Press.Google Scholar
Smith, G. & Grenfell, B. T. (1994). Modelling of parasitic populations: gastrointestinal nematode models. Veterinary Parasitology 54, 127–34.CrossRefGoogle ScholarPubMed
Southwood, T. R. E. (1978). Ecological Methods. 2nd Edn, New York: Wiley.Google Scholar