Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-28T06:19:48.169Z Has data issue: false hasContentIssue false
  • English
  • Français

Population dynamics in echinococcosis and cysticercosis: mathematical model of the life-cycle of Echinococcus granulosus

Published online by Cambridge University Press:  06 April 2009

M. G. Roberts ,
J. R. Lawson  and
M. A. Gemmell
M. G. Roberts
Affiliation:
Wallaceville Animal Research Centre, Research Division, Ministry of Agriculture and Fisheries, Upper Hutt, New Zealand
J. R. Lawson
Affiliation:
Research Unit, Research Division, Ministry of Agriculture and Fisheries, University of Otago Medical School, Dunedin, New Zealand
M. A. Gemmell
Affiliation:
Research Unit, Research Division, Ministry of Agriculture and Fisheries, University of Otago Medical School, Dunedin, New Zealand
Get access Rights & Permissions [Opens in a new window]

Summary

A mathematical model of the life-cycle of Echinococcus granulosus in dogs and sheep in New Zealand is constructed and used to discuss previously published experimental and survey data. The model is then used to describe the dynamics of transmission of the parasite, and the means by which it may be destabilized. It is found that under the conditions that prevailed in New Zealand during the late 1950s, at the time of surveys of this parasite, the dog–sheep life-cycle was not regulated by any effective density-dependent constraint. In contrast there was evidence for an effective acquisition of immunity to reinfection by cattle. The long time to maturity of the cyst in sheep, together with the practice of feeding aged sheep to dogs, provides a time delay in the intermediate host. By comparison, the time to maturity of the adult stage in dogs is short, but it is of sufficient magnitude to be a key factor in the destabilization of the system by a regular dog-dosing programme. The model used to describe the life-cycle is a linear integrodifferential equation of the Volterra type. Such equations are intrinsically unstable in that a small perturbation in parameters can drive a previous equilibrium solution to zero. At the time of the surveys, the value of the basic reproductive rate, R0 was close to 1, and it has since been reduced below 1 by control measures.

Type
Research Article
Information
Parasitology , Volume 92 , Issue 3 , June 1986 , pp. 621 - 641
Copyright
Copyright © Cambridge University Press 1986

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. (1974). Population dynamics of the cestode Caryophyllaeus laticeps (Pallas, 1781) in the bream (Abramis brama L.). Journal of Animal Ecology 43, 305–21.CrossRefGoogle Scholar
Anderson, R. M. (1978). Population dynamics of snail infection by miracidia. Parasitology 77, 201–24.CrossRefGoogle ScholarPubMed
Anderson, R. M. (1982 a). The Population Dynamics of Infectious Diseases: Theory and Applications. London and New York: Chapman and Hall.Google Scholar
Anderson, R. M. (1982 b). Transmission dynamics and control of infectious disease agents. In Population Biology of Infectious Diseases (ed. Anderson, R. M. and May, R. M.), pp. 149–76. Berlin, Heidelberg, New York: Springer-Verlag.CrossRefGoogle Scholar
Anderson, R. M. & May, R. M. (1978). Regulation and stability of host–parasite population interactions. 1. Regulatory processes. Journal of Animal Ecology 47, 219–47.CrossRefGoogle Scholar
Anderson, R. M. & May, R. M. (1982 a). Population dynamics of human helminth infections: control by chemotherapy. Nature, London 297, 557–63.CrossRefGoogle ScholarPubMed
Anderson, R. M. & May, R. M. (1982 b). Population Biology of Infectious Diseases. Berlin, Heidelberg, New York: Springer-Verlag.CrossRefGoogle Scholar
Aron, J. L. (1983). Dynamics of acquired immunity boosted by exposure to infection. Mathematical Biosciences 64, 249–59.CrossRefGoogle Scholar
Bartlett, M. S. (1960). Stochastic Population Models in Ecology and Epidemiology. London: Methuen.Google Scholar
Bliss, C. I. & Owen, A. R. G. (1958). Negative binomial distributions with a common k. Biometrika 45, 37–58.CrossRefGoogle Scholar
Boray, J. C. (1969). Experimental fascioliasis in Australia. Advances in Parasitology 7, 96–210.Google ScholarPubMed
Bradley, D. J. (1972). Regulation of parasite populations. Transactions of the Royal Society of Tropical Medicine and Hygiene 66, 697–708.CrossRefGoogle ScholarPubMed
Cushing, J. M. (1977). Integrodifferential equations and delay models in population dynamics. Lecture Notes in Biomathematics 20.CrossRefGoogle Scholar
Fisher, R. A., Corbett, A. S. & Williams, C. B. (1943). The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology 12, 42–58.CrossRefGoogle Scholar
Friis, A. L., Sayers, E. & McLean, J. W. (1967). Report of the Committee of Inquiry into Hydatids Eradication. Government Printer, Wellington, New Zealand.Google Scholar
Froyd, G. (1960). Cysticercosis and hydatid disease of cattle in Kenya. Journal of Parasitology 46, 491–6.CrossRefGoogle ScholarPubMed
Gemmell, M. A. (1957). Hydatid diseases in Australia. II. Observations on the geographical distribution of Echinococcus granulosu (Batsch, 1786) (Rudolphi, 1805) in the dog in New South Wales. Australian Veterinary Journal 33, 217–26.CrossRefGoogle Scholar
Gemmell, M. A. (1958). Cestode problems of domestic animals and man in the South Island of New Zealand. New Zealand Medical Journal 42, 442–58.Google Scholar
Gemmell, M. A. (1959). Hydatid diseases in Australia. IV. Observations on the incidence of Echinococcus granulosus on stations and farms in endemic regions of New South Wales. Australian Veterinary Journal 35, 396–402.CrossRefGoogle Scholar
Gemmell, M. A. (1961). An analysis of the incidence of hydatid cysts (Echinococcus granulosus) in domestic food animals in New Zealand, 1958–1959. New Zealand Veterinary Journal 9, 29–37.CrossRefGoogle Scholar
Gemmell, M. A. (1962). Natural and acquired immunity factors interfering with development during the rapid growth phase of Echinococcus granulosus in dogs. Immunology 5, 496–503.Google ScholarPubMed
Gemmell, M. A. (1973). Hydatid disease in New Zealand. The first hundred years (1873–1972). In Recent Advances in Hydatid Disease. Proceedings of a Symposium of the Hamilton Medical Veterinary Association (ed. Brown, R. W.Salisbury, T. R. and White, W. E.), pp. 54–61. Hamilton, Victoria.Google Scholar
Gemmell, M. A. (1977). Taeniidae: modification to the life span of the egg and the regulation of tapeworm populations. Experimental Parasitology 41, 314–28.CrossRefGoogle Scholar
Gemmell, M. A. & Johnstone, P. D. (1976). Factors regulating tapeworm populations: dispersion of eggs of Taenia hydatigena on pasture. Annals of Tropical Medicine and Parasitology 70, 431–4.CrossRefGoogle ScholarPubMed
Gemmell, M. A. & Johnstone, P. D. (1981). Factors regulating tapeworm populations: estimations of the duration of acquired immunity by sheep to Taenia hydatigena. Research in Veterinary Science 30, 53–6.CrossRefGoogle ScholarPubMed
Gemmell, M. A. & Lawson, J. R. (1984). Epidemiology and control of hydatid disease. In The Biology of Echinococcus and Hydatid Disease (ed. Thompson, R. C. A.). Boston, London and Sydney: George Allen and Unwin. (In the Press.)Google Scholar
Gemmell, M. A., Lawson, J. R. & Roberts, M. G. (1986). Population dynamics in echinococcosis and cysticercosis: biological parameters of Echinococcus granulosus in dogs and sheep. Parasitology 92, 599–620.CrossRefGoogle ScholarPubMed
Harris, R. E., Revfeim, K. J. A. & Heath, D. D. (1980). Simulating strategies for control of Echinococcus granulosus, Taenia hydatigena and T. ovis. Journal of Hygiene 84, 389–404.CrossRefGoogle ScholarPubMed
Jackson, P. J. & Arundel, J. H. (1971). The incidence of tapeworms in rural dogs in Victoria. Australian Veterinary Journal 47, 46–53.CrossRefGoogle ScholarPubMed
Keymer, A. (1982 a). Tapeworm infections. In The Population Dynamics of Infectious Diseases: Theory and Applications, (ed. Anderson, R. M.), pp. 109–138. London and New York: Chapman and Hall.CrossRefGoogle Scholar
Keymer, A. (1982 b). Density-dependent mechanisms in the regulation of intestinal helminth populations. Parasitology 84, 573–87.CrossRefGoogle ScholarPubMed
Lawson, J. R. & Gemmell, M. A. (1983). Hydatidosis and cysticercosis: the dynamics of transmission. Advances in Parasitology 22, 261–308.CrossRefGoogle ScholarPubMed
Lawson, J. R. & Gemmell, M. A. (1985). The potential role of blowflies in the transmission of taeniid tapeworm eggs. Parasitology 91, 129–43.CrossRefGoogle ScholarPubMed
May, R. M. & Anderson, R. M. (1978). Regulation and stability of host–parasite population interactions. II. Destabilizing processes. Journal of Animal Ecology 47, 249–67.CrossRefGoogle Scholar
Nisbet, R. M. & Gurney, W. S. C. (1982). Modelling Fluctuating Populations. Chichester, New York, Brisbane, Toronto, Singapore: Wiley.Google Scholar
Pullar, E. M. & Marshall, W. K. (1958). The incidence of hydatids in Victorian cattle. Australian Veterinary Journal 34, 193–201.CrossRefGoogle Scholar
Southwood, T. R. E. (1978). Ecological Methods, 2nd edn. London: Chapman and Hall.Google Scholar
Sweatman, G. K., Williams, R. J., Moriarty, K. M. & Henshall, T. C. (1963). On acquired immunity to Echinococcus granulosus in sheep. Research in Veterinary Science 4, 187–98.CrossRefGoogle Scholar
Weiss, G. H. & Aron, J. L. (1983). Note on the formulation of a stochastic model of superinfection. Mathematical Biosciences 67, 213–23.CrossRefGoogle Scholar