Modelling Stochastic Transmission Processes in Helminth Infections

  • Stephen J. Cornell
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 673)


The number of helminths within a host can only increase by the host encountering additional infectious stages, so it is important to consider not only whether a host is infected, but also the severity of its infection. Stochastic models consider explicitly the number of parasites within the host and treat infection, death and other demographic events as random processes. I discuss stochastic helminth population models of increasing degrees of complexity, starting with the infection dynamics within a single host and finishing with the full parasite lifecycle among a population of hosts. I demonstrate the mathematical techniques that can help to analyse these models and discuss the insights into parasite population biology that these methods can bring.


Host Population Helminth Infection Parasite Population Worm Burden Probability Generate Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Anderson RM, May RM. Infectious Diseases of Humans. Oxford: Oxford University Press, 1991.Google Scholar
  2. 2.
    May RM. Togetherness among schistosomes: its effects on the dynamics of the infection. Math Biosci 1977; 35:301–343.CrossRefGoogle Scholar
  3. 3.
    Woolhouse MEJ. A theoretical framework for the immunoepidemiology of helminth infection. Parasite Imunol 1992; 14:563–578.CrossRefGoogle Scholar
  4. 4.
    Shaw DJ, Dobson AP. Patterns of macroparasite abundance and aggregation in wildlife populations: a quantitative review. Parasitology 1995; 111:S111–S133.CrossRefPubMedGoogle Scholar
  5. 5.
    Marion G, Renshaw E, Gibson G. Stochastic modelling of environmental variation for biological populations. Theor Popul Biol 2000; 57:197–217.CrossRefPubMedGoogle Scholar
  6. 6.
    Morgan ER, Medley GF, Torgerson PR et al. Parasite transmission in a migratory multiple host system. Ecol Modell 2007; 200:511–520.CrossRefGoogle Scholar
  7. 7.
    Anderson RM, May RM. Regulation and stability of host-parasite population interactions: I. regulatory processes. J Anim Ecol 1978; 47:219–247.CrossRefGoogle Scholar
  8. 8.
    May RM, Anderson RM. Regulation and stability of host-parasite population interactions: II. destabilizing processes. J Anim Ecol 1978; 47:249–267.CrossRefGoogle Scholar
  9. 9.
    Anderson RM, Gordon DM. Processes influencing the distribution of parasite numbers within host populations special emphasis on parasite-induced mortalities. Parasitology 1982; 85:373–398.CrossRefPubMedGoogle Scholar
  10. 10.
    Isham VS. Stochastic models of host-macroparasite interaction. Ann Appl Probab 1995; 5:197–210.CrossRefGoogle Scholar
  11. 11.
    Rosà R, Pugliese A. Aggregation, stability and oscillations in different models for host—macroparasite interactions. Theor Popul Biol 2002; 61:319–334.CrossRefPubMedGoogle Scholar
  12. 12.
    Rosà R, Pugliese A, Villani A et al. Individual-based vs. deterministic models for macroparasites: host cycles and extinction. Theor Popul Biol 2003; 63:295–307.CrossRefPubMedGoogle Scholar
  13. 13.
    Tallis GM, Leyton M. Stochastic models of populations of helminthic parasites in the definitive host. Math Biosci 1969; 4:39–48.CrossRefGoogle Scholar
  14. 14.
    Herbert J, Isham VS. Stochastic host-parasite interaction models. J Math Biol 2000; 40:343–371.CrossRefPubMedGoogle Scholar
  15. 15.
    Barbour AD, Pugliese A. On the variance-to-mean ratio in models of parasite distributions. Adv Appl Probab 2000; 32:701–719.CrossRefGoogle Scholar
  16. 16.
    Hudson PJ, Dobson AP. Macroparasites: observed patterns in naturally fluctuating animal populations. In: Grenfell BT, Dobson AP, eds. Ecology Of Infectious Diseases In Natural Populations. Cambridge: Cambridge University Press, 1995.Google Scholar
  17. 17.
    Chan MS, Isham VS. A stochastic model of schistosomiasis immuno-epidemiology. Math Biosci 1998; 151:179–198.CrossRefPubMedGoogle Scholar
  18. 18.
    Grenfell BT, Wilson K, Isham VS et al. Modelling patterns of parasite aggregation in natural populations: trichostrongylid nematode-ruminant interactions as a case study. Parasitology 1995; 111:S135–S151.CrossRefPubMedGoogle Scholar
  19. 19.
    Chan MS, Mutapi F, Woolhouse MEJ et al. Stochastic simulations and the detection of immunity to schistosome infections. Parasitology 2000; 120:161–169.CrossRefPubMedGoogle Scholar
  20. 20.
    Cornell SJ, Isham VS, Grenfell BT. Drug resistant parasites and aggregated infection—early-season dynamics. J Math Biol 2000; 41:341–360.CrossRefPubMedGoogle Scholar
  21. 21.
    Lello J, Fenton A, Stevenson IR et al. Competition and mutualism among the gut helminths of a mammalian host. Nature 2004; 428:840–844.CrossRefPubMedGoogle Scholar
  22. 22.
    Bottomley C, Isham V, Basanez MG. Population biology of multispecies helminth infection: interspecific interactions and parasite distribution. Parasitology 2005; 131:417–433.CrossRefPubMedGoogle Scholar
  23. 23.
    Nåsell I. Hybrid Models of Tropical Infections. Berlin: Springer-Verlag, 1985.Google Scholar
  24. 24.
    Kretzschmar M, Adler FR. Aggregated distributions in models for patchy populations. Theor Popul Biol 1993; 43:1–30.CrossRefPubMedGoogle Scholar
  25. 25.
    Anderson RM, May RM, Gupta S. Nonlinear phenomena in host-parasite interactions. Parasitology 1989; 99:S59–S79.CrossRefPubMedGoogle Scholar
  26. 26.
    Churcher TS, Ferguson NM, Basanez MG. Density dependence and overdispersion in the transmission of helminth parasites. Parasitology 2005; 131:121–132.CrossRefPubMedGoogle Scholar
  27. 27.
    Churcher TS, Filipe JAN, Basanez MG. Density dependence and the control of helminth parasites. J Anim Ecol 2006; 75:1313–1320.CrossRefPubMedGoogle Scholar
  28. 28.
    Churcher TS, Basanez MG. Density dependence and the spread of anthelmintic resistance. Evolution 2008; 62:528–537.CrossRefPubMedGoogle Scholar
  29. 29.
    Bottomley C, Isham V, Basanez MG. Population biology of multispecies helminth infection: Competition and coexistence. J Theor Biol 2007; 244:81–95.CrossRefPubMedGoogle Scholar
  30. 30.
    Saul A. Computer model of the maintenance and selection of genetic heterogeneity in polygamous helminths. Parasitology 1995; 111:531–536.CrossRefPubMedGoogle Scholar
  31. 31.
    Plaisier AP, Subramanian S, Das PK et al. The lymfasim simulation program for modeling lymphatic filariasis and its control. Methods Inf Med 1998; 37:97–108.PubMedGoogle Scholar
  32. 32.
    Vlas SJ, Van Oortmarssen GJ, Gryseels B et al. Schistosim: a microsimulation model for the epidemiology and control of schistosomiasis. Parasitology 1996; 55:170–175.Google Scholar
  33. 33.
    Cornell SJ, Isham VS. Ultimate extinction of the promiscuous bisexual galton-watson metapopulation. Aust N Z J Stat 2004; 46:87–98.CrossRefGoogle Scholar
  34. 34.
    Cornell SJ, Isham VS, Grenfell BT. Stochastic and spatial dynamics of nematode parasites in farmed ruminants. Proc R Soc Lond B Biol Sci 2004; 271:1243–1250.CrossRefGoogle Scholar
  35. 35.
    Allee WC. Animal Aggregations: a study in general sociology. Chicago: University of Chicago Press, 1931.Google Scholar
  36. 36.
    Cornell SJ, Grenfell BT. Spatiotemporal infection dynamics and the evolution of drug resistance in nematode parasites of ruminants. In: Poulin R, Morand S, Skorping A, eds., Evolutionary Biology Of Host-Parasite Relationships: Theory Meets Reality. Elsevier, 2000.Google Scholar
  37. 37.
    Cornell SJ, Isham VS, Smith G et al. Spatial parasite transmission, drug resistance and the spread of rare genes. Proc Natl Acad Sci USA 2003; 100:7401–7405.CrossRefPubMedGoogle Scholar
  38. 38.
    Cornell SJ, Bjornstad ON, Cattadori IM et al. Seasonality, cohort-dependence and the development of immunity in a natural host-nematode system. Proc R Soc Lond B Biol Sci 2008; 275:511–518.CrossRefGoogle Scholar
  39. 39.
    Marion G, Renshaw E, Gibson G. Stochastic effects in nematode infections of ruminants. IMA J Math Appl Med Biol 1998; 15:97–116.CrossRefPubMedGoogle Scholar
  40. 40.
    Ross JV. A stochastic metapopulation model accounting for habitat dynamics. J Math Biol 2006; 52:788–806.CrossRefPubMedGoogle Scholar
  41. 41.
    Ovaskainen O, Cornell SJ. Space and stochasticity in population dynamics. Proc Natl Acad Sci USA 2006; 103:12781–12786.CrossRefPubMedGoogle Scholar

Copyright information

© Landes Bioscience and Springer Science+Business Media 2010

Authors and Affiliations

  • Stephen J. Cornell
    • 1
  1. 1.Institute of Integrative and Comparative BiologyUniversity of LeedsLeedsUK

Personalised recommendations