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. 2004 Jun 22;271(1545):1243–1250. doi: 10.1098/rspb.2004.2744

Stochastic and spatial dynamics of nematode parasites in farmed ruminants.

Stephen J Cornell 1, Valerie S Isham 1, Bryan T Grenfell 1
PMCID: PMC1691719  PMID: 15306348

Abstract

Host-parasite systems provide powerful opportunities for the study of spatial and stochastic effects in ecology; this has been particularly so for directly transmitted microparasites. Here, we construct a fully stochastic model of the population dynamics of a macroparasite system: trichostrongylid gastrointestinal nematode parasites of farmed ruminants. The model subsumes two implicit spatial effects: the host population size (the spatial extent of the interaction between hosts) and spatial heterogeneity ('clumping') in the infection process. This enables us to investigate the roles of several different processes in generating aggregated parasite distributions. The necessity for female worms to find a mate in order to reproduce leads to an Allee effect, which interacts nonlinearly with the stochastic population dynamics and leads to the counter-intuitive result that, when rare, epidemics can be more likely and more severe in small host populations. Clumping in the infection process reduces the strength of this Allee effect, but can hamper the spread of an epidemic by making infection events too rare. Heterogeneity in the hosts' response to infection has to be included in the model to generate aggregation at the level observed empirically.

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Selected References

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  1. Adler F. R., Kretzschmar M. Aggregation and stability in parasite-host models. Parasitology. 1992 Apr;104(Pt 2):199–205. doi: 10.1017/s0031182000061631. [DOI] [PubMed] [Google Scholar]
  2. Anderson R. M., Gordon D. M. Processes influencing the distribution of parasite numbers within host populations with special emphasis on parasite-induced host mortalities. Parasitology. 1982 Oct;85(Pt 2):373–398. doi: 10.1017/s0031182000055347. [DOI] [PubMed] [Google Scholar]
  3. Anderson R. M., May R. M. Coevolution of hosts and parasites. Parasitology. 1982 Oct;85(Pt 2):411–426. doi: 10.1017/s0031182000055360. [DOI] [PubMed] [Google Scholar]
  4. Anderson R. M., May R. M. Herd immunity to helminth infection and implications for parasite control. Nature. 1985 Jun 6;315(6019):493–496. doi: 10.1038/315493a0. [DOI] [PubMed] [Google Scholar]
  5. Barbour A. D., Kafetzaki M. Modeling the overdispersion of parasite loads. Math Biosci. 1991 Dec;107(2):249–253. doi: 10.1016/0025-5564(91)90008-7. [DOI] [PubMed] [Google Scholar]
  6. Barger I. A. The statistical distribution of trichostrongylid nematodes in grazing lambs. Int J Parasitol. 1985 Dec;15(6):645–649. doi: 10.1016/0020-7519(85)90010-4. [DOI] [PubMed] [Google Scholar]
  7. Berding C., Keymer A. E., Murray J. D., Slater A. F. The population dynamics of acquired immunity to helminth infection. J Theor Biol. 1986 Oct 21;122(4):459–471. doi: 10.1016/s0022-5193(86)80186-2. [DOI] [PubMed] [Google Scholar]
  8. Cornell S. J., Isham V. S., Grenfell B. T. Drug-resistant parasites and aggregated infection--early-season dynamics. J Math Biol. 2000 Oct;41(4):341–360. doi: 10.1007/s002850000051. [DOI] [PubMed] [Google Scholar]
  9. Cornell S. J., Isham V. S., Smith G., Grenfell B. T. Spatial parasite transmission, drug resistance, and the spread of rare genes. Proc Natl Acad Sci U S A. 2003 May 27;100(12):7401–7405. doi: 10.1073/pnas.0832206100. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Coyne M. J., Smith G., Johnstone C. Fecundity of gastrointestinal trichostrongylid nematodes of sheep in the field. Am J Vet Res. 1991 Jul;52(7):1182–1188. [PubMed] [Google Scholar]
  11. Grenfell B. T., Smith G., Anderson R. M. A mathematical model of the population biology of Ostertagia ostertagi in calves and yearlings. Parasitology. 1987 Oct;95(Pt 2):389–406. doi: 10.1017/s0031182000057826. [DOI] [PubMed] [Google Scholar]
  12. Grenfell B. T., Smith G., Anderson R. M. Maximum-likelihood estimates of the mortality and migration rates of the infective larvae of Ostertagia ostertagi and Cooperia oncophora. Parasitology. 1986 Jun;92(Pt 3):643–652. doi: 10.1017/s0031182000065501. [DOI] [PubMed] [Google Scholar]
  13. Grenfell B. T., Smith G., Anderson R. M. The regulation of Ostertagia ostertagi populations in calves: the effect of past and current experience of infection on proportional establishment and parasite survival. Parasitology. 1987 Oct;95(Pt 2):363–372. doi: 10.1017/s0031182000057802. [DOI] [PubMed] [Google Scholar]
  14. Grenfell B. T., Wilson K., Isham V. S., Boyd H. E., Dietz K. Modelling patterns of parasite aggregation in natural populations: trichostrongylid nematode-ruminant interactions as a case study. Parasitology. 1995;111 (Suppl):S135–S151. doi: 10.1017/s0031182000075867. [DOI] [PubMed] [Google Scholar]
  15. Gruner L., Mauleon H., Sauve C. Migrations of trichostrongyle infective larvae experiments with ovine parasites in soil. Ann Rech Vet. 1982;13(1):51–59. [PubMed] [Google Scholar]
  16. Gruner L., Sauve C. The distribution of trichostrongyle infective larvae on pasture and grazing behaviour in calves. Vet Parasitol. 1982 Nov;11(2-3):203–213. doi: 10.1016/0304-4017(82)90043-7. [DOI] [PubMed] [Google Scholar]
  17. Heesterbeek J. A., Roberts M. G. Threshold quantities for helminth infections. J Math Biol. 1995;33(4):415–434. doi: 10.1007/BF00176380. [DOI] [PubMed] [Google Scholar]
  18. Herbert J., Isham V. Stochastic host-parasite interaction models. J Math Biol. 2000 Apr;40(4):343–371. doi: 10.1007/s002850050184. [DOI] [PubMed] [Google Scholar]
  19. Kao R. R., Leathwick D. M., Roberts M. G., Sutherland I. A. Nematode parasites of sheep: a survey of epidemiological parameters and their application in a simple model. Parasitology. 2000 Jul;121(Pt 1):85–103. doi: 10.1017/s0031182099006095. [DOI] [PubMed] [Google Scholar]
  20. Kretzschmar M., Adler F. R. Aggregated distributions in models for patchy populations. Theor Popul Biol. 1993 Feb;43(1):1–30. doi: 10.1006/tpbi.1993.1001. [DOI] [PubMed] [Google Scholar]
  21. Kretzschmar M. Persistent solutions in a model for parasitic infections. J Math Biol. 1989;27(5):549–573. doi: 10.1007/BF00288434. [DOI] [PubMed] [Google Scholar]
  22. Marion G., Renshaw E., Gibson G. Stochastic effects in a model of nematode infection in ruminants. IMA J Math Appl Med Biol. 1998 Jun;15(2):97–116. [PubMed] [Google Scholar]
  23. May R. M., Anderson R. M. Parasite-host coevolution. Parasitology. 1990;100 (Suppl):S89–101. doi: 10.1017/s0031182000073042. [DOI] [PubMed] [Google Scholar]
  24. Michael E., Bundy D. A., Grenfell B. T. Re-assessing the global prevalence and distribution of lymphatic filariasis. Parasitology. 1996 Apr;112(Pt 4):409–428. doi: 10.1017/s0031182000066646. [DOI] [PubMed] [Google Scholar]
  25. Michel J. F. The epidemiology and control of some nematode infections in grazing animals. Adv Parasitol. 1976;14:355–397. doi: 10.1016/s0065-308x(08)60517-5. [DOI] [PubMed] [Google Scholar]
  26. Pacala S. W., Dobson A. P. The relation between the number of parasites/host and host age: population dynamic causes and maximum likelihood estimation. Parasitology. 1988 Feb;96(Pt 1):197–210. doi: 10.1017/s0031182000081762. [DOI] [PubMed] [Google Scholar]
  27. Pugliese A., Rosà R., Damaggio M. L. Analysis of model for macroparasitic infection with variable aggregation and clumped infections. J Math Biol. 1998 Apr;36(5):419–447. doi: 10.1007/s002850050107. [DOI] [PubMed] [Google Scholar]
  28. Roberts M. G., Grenfell B. T. The population dynamics of nematode infections of ruminants: periodic perturbations as a model for management. IMA J Math Appl Med Biol. 1991;8(2):83–93. doi: 10.1093/imammb/8.2.83. [DOI] [PubMed] [Google Scholar]
  29. Roberts M. G., Grenfell B. T. The population dynamics of nematode infections of ruminants: the effect of seasonality in the free-living stages. IMA J Math Appl Med Biol. 1992;9(1):29–41. doi: 10.1093/imammb/9.1.29. [DOI] [PubMed] [Google Scholar]
  30. Roberts M. G. Mathematical models for nematode parasites of ruminants. Parasitol Today. 1991 Jan;7(1):4–4. doi: 10.1016/0169-4758(91)90075-y. [DOI] [PubMed] [Google Scholar]
  31. Roberts M. G. The immunoepidemiology of nematode parasites of farmed animals: a mathematical approach. Parasitol Today. 1999 Jun;15(6):246–251. doi: 10.1016/s0169-4758(99)01430-1. [DOI] [PubMed] [Google Scholar]
  32. Saul A. Computer model of the maintenance and selection of genetic heterogeneity in polygamous helminths. Parasitology. 1995 Nov;111(Pt 4):531–536. doi: 10.1017/s003118200006604x. [DOI] [PubMed] [Google Scholar]
  33. Shaw D. J., Dobson A. P. Patterns of macroparasite abundance and aggregation in wildlife populations: a quantitative review. Parasitology. 1995;111 (Suppl):S111–S127. doi: 10.1017/s0031182000075855. [DOI] [PubMed] [Google Scholar]
  34. Smith G., Grenfell B. T., Anderson R. M., Beddington J. Population biology of Ostertagia ostertagi and anthelmintic strategies against ostertagiasis in calves. Parasitology. 1987 Oct;95(Pt 2):407–420. doi: 10.1017/s0031182000057838. [DOI] [PubMed] [Google Scholar]
  35. Smith G., Grenfell B. T., Anderson R. M. The development and mortality of the non-infective free-living stages of Ostertagia ostertagi in the field and in laboratory culture. Parasitology. 1986 Apr;92(Pt 2):471–482. doi: 10.1017/s0031182000064222. [DOI] [PubMed] [Google Scholar]
  36. Smith G., Grenfell B. T., Anderson R. M. The regulation of Ostertagia ostertagi populations in calves: density-dependent control of fecundity. Parasitology. 1987 Oct;95(Pt 2):373–388. doi: 10.1017/s0031182000057814. [DOI] [PubMed] [Google Scholar]
  37. Smith G., Grenfell B. T., Isham V., Cornell S. Anthelmintic resistance revisited: under-dosing, chemoprophylactic strategies, and mating probabilities. Int J Parasitol. 1999 Jan;29(1):77–94. doi: 10.1016/s0020-7519(98)00186-6. [DOI] [PubMed] [Google Scholar]
  38. Smith G. The population biology of the parasitic stages of Haemonchus contortus. Parasitology. 1988 Feb;96(Pt 1):185–195. doi: 10.1017/s0031182000081750. [DOI] [PubMed] [Google Scholar]

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