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Changes in parasite aggregation with age: a discrete infection model

  • R. J. Quinnell (a1), A. Grafen (a2) and M. E. J. Woolhouse (a3)

We present a discrete time model for age-related changes in the mean and variance of the number of helminth parasites per host. We assess the degree of aggregation as the negative binomial parameter, k, and use the model to examine the influence of various factors on changes in aggregation with host age: discrete versus continuous infection; the degree of predisposition to infection; infection rate; parasite survival rate; and the variance in exposure to infective stages. The model can produce both increases and decreases in k with host age. However, with parameter values typical of many human helminth infections, a monotonic increase in k (decrease in aggregation) with age is predicted. With an age-dependent infection rate, convex relationships between k and age are possible. These predictions are consistent with data from field studies, but differ from those of previous models which have suggested that k is independent of host age in the absence of density dependence in parasite population dynamics. Differences between the models, and some difficulties in the interpretation of field data, are discussed.

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Anderson R. M. (1974). Mathematical models of host-helminth parasite interactions. In Ecological Stability (ed. Usher M. B. & Williamson M. H.), pp. 4369. London: Chapman and Hall.
Anderson R. M. (1980). The dynamics and control of direct life cycle helminth parasites. Lecture Notes in Biomathematics 39, 278322.
Anderson R. M. (1985). Mathematical models in the study of the epidemiology and control of ascariasis in man. In Ascariasis and its Public Health Importance (ed. Crompton D. W. T., Nesheim M. C. & Pawlowski Z. S.), pp. 3967. London: Taylor & Francis.
Anderson R. M. & Gordon D. M. (1982). Processes influencing the distribution of parasite numbers within host populations with special emphasis on parasite-induced host mortalities. Parasitology 85, 373–98.
Anderson R. M. & May R. M. (1985 a). Helminth infections of humans: mathematical models population dynamics and control. Advances in Parasitology 24, 1101.
Anderson R. M. & May R. M. (1985 b). Herd immunity to helminth infection and implications for parasite control. Nature, London 315, 493–6.
Anderson R. M. & May R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press.
Bradley D. J. & McCullough F. S. (1973). Egg Output stability and the epidemiology of Schistosoma haematobium. Part II. An analysis of the epidemiology of S. haematobium. Transactions of the Royal Society of Tropical Medicine and Hygiene 67, 491500.
Brattey J. & I-Hsun ni (1992). Ascaridoid nematodes from the stomach of harp seals, Phoca groenlandica, from Newfoundland and Labrador. Canadian Journal of Fisheries and Aquatic Science 49, 956–66.
Bundy D. A. P., Cooper E. S., Thompson D. E., Anderson R. M. & Didier J. M. (1987). Age-related prevalences and intensity of Trichuris trichiura infection in a St. Lucian community. Transactions of the Royal Society of Tropical Medicine and Hygiene 81, 8594.
Bundy D. A. P., Kan S. P. & Rose R. (1988). Age-related prevalence, intensity and frequency distribution of gastrointestinal helminth infection in urban slum children from Kuala Lumpur Malaysia. Transactions of the Royal Society of Tropical Medicine and Hygiene 82, 289–94.
Chandiwana S. K. (1987). Analysis of the Dynamics of Transmission of Human Schistosomiasis in Two Rural Communities in Zimbabwe. Ph.D. thesis, University of Zimbabwe.
Chandiwana S. K. (1990). Hookworm population ecology in Zimbabwe. In Hookworm Disease: Current Status and New Directions (ed. Schad G. A. & Warren K. S.), pp. 165176. London: Taylor & Francis.
Chandiwana S. K., Christensen N. O. & Frandsen F. (1987). Seasonal patterns in the transmission of Schistosoma haematobium, S. mattheei and S. mansoni in the highveld region of Zimbabwe. Acta Tropica 44, 433–44.
Chandiwana S. K. & Woolhouse M. E. J. (1991). Heterogeneities in water contact patterns and the epidemiology of Schistosoma haematobium. Parasitology 103, 363–70.
Croll N. A., Anderson R. M., Gyarkos T. W. & Ghadirian E. (1982). The population biology and control of Ascaris lumbricoides in a rural community in Iran. Transactions of the Royal Society of Tropical Medicine and Hygiene 76, 187–97.
de Vlas S. J., Gryseels B., Van Oortmarssen G. J., Polderman A. M. & Habbema J. D. F. (1992). A model for variations in single and repeated egg counts in Schistosoma mansoni infections. Parasitology 104, 451–60.
Dietz K. (1988). Mathematical models. In Malaria, Vol. 2 (ed. Wernsdorfer W. H. & McGregor I.), pp. 1091–134 Edinburgh: Churchill-Livingstone.
Dobson A. P., Pacala S. V., Roughgarden J. D., Carper E. R. & Harris E. A. (1992). The parasites of anolis lizards in the northern Lesser Antilles. 1. Patterns of distribution and abundance. Oecologia 91, 110–17.
Elkins D. B., Haswell-Elkins M. R. & Anderson R. M. (1988). The importance of host age and sex to patterns of reinfection with Ascaris lumbricoides following mass anthelminthic treatment in a South Indian fishing community. Parasitology 96, 171–84.
Fulford A. J. C., Butterworth A. E., Sturrock R. F. & Ouma J. H. (1992). On the use of age-intensity data to detect immunity to parasitic infections with special reference to Schistosoma mansoni in Kenya. Parasitology 105, 219–28.
Grafen A. & Woolhouse M. E. J. (1993). Does the negative binomial distribution add up ? Parasitology Today 9, 475–7.
Gregory R. D. (1992). On the interpretation of host-parasite ecology: Heligmosomoides polygyrus (Nematoda) in wild wood mouse (Apodemus sylvaticus) populations. Journal of Zoology 226, 109–21.
Gregory R. D. & Woolhouse M. E. J. (1993). Quantification of parasite aggregation: a simulation study. Acta Tropica 54, 131–9.
Grenfell B. T., Dietz K. & Roberts M. G. (1995). Modelling the immuno-epidemiology of macroparasites in naturally-fluctuating host populations. In Ecology of Infectious Diseases in Natural Populations (ed. Grenfell B. T. & Dobson A. P.), pp. 362383. Cambridge: Cambridge University Press.
Hadeler K. P. & Dietz K. (1983). Nonlinear hyperbolic partial differential equations for the dynamics of parasite populations. Computers and Mathematics with Applications 9, 415–30.
Haswell-Elkins M. R., Elkins D. B., Manjula K., Michael E. & Anderson R. M. (1988). An investigation of hookworm infection and reinfection following mass anthelminthic treatment in the South Indian fishing community of Vairavankuppam. Parasitology 96, 565–77.
Hominick W. M., Dean C. G. & Schad G. A. (1987). Population biology of hookworms in West Bengal: analysis of infective larvae recovered from damp pads applied to the soil surface at defaecation sites. Transactions of the Royal Society of Tropical Medicine and Hygiene 81, 978–86.
Keymer A. E. & Pagel M. (1990). Predisposition to helminth infection. In Hookworm Disease: Current Status and New Directions (ed. Schad G. A. & Warren K. S.), pp. 177209. London: Taylor & Francis.
Pacala S. W. & Dobson A. P. (1988). The relation between the number of parasites/host and host age: population dynamic causes and maximum likelihood estimation. Parasitology 96, 197210.
Quinnell R. J. (1992). The population dynamics of Heligmosomoides polygyrus in an enclosure population of wood mice. Journal of Animal Ecology 61, 669–79.
Quinnell R. J., Slater A. F. G., Tighe P., Walsh E. A., Keymer A. E. & Pritchard D. I. (1993). Reinfection with hookworm after chemotherapy in Papua New Guinea. Parasitology 106, 379–85.
Srividya A., Krishnamoorthy K., Sabesan S., Panicker A. N., Grenfell B. T. & Bundy D. A. P. (1991). Frequency distribution of Brugia malayi microfilariae in human populations. Parasitology 102, 207–12.
Sweet W. C. (1925). Average egg count per gm faeces per female hookworm in Ceylon. Journal of Parasitology 12, 3942.
Taylor L. R., Woiwod I. P. & Perry J. N. (1979). The negative binomial as a dynamic ecological model for aggregation and the density dependence of k. Journal of Animal Ecology 48, 289304.
Tinsley R. C. & Jackson H. C. (1988). Pulsed transmission of Pseudodiplorchis americanus (Monogenea) between desert hosts (Scaphiopus couchii). Parasitology 97, 437–53.
Udonsi J. K. (1990). Human community ecology of urinary schistosomiasis in relation to snail vector bionomics in the Igwun river basin of Nigeria. Tropical Medicine and Parasitology 41, 131–5.
Warren K. S., Mahmoud A. A. F., Cummings P., Murphy D. J. & Houser D. B. (1974). Schistosomiasis mansoni in Yemeni in California: duration of infection, presence of disease and therapeutic management. American Journal of Tropical Medicine and Hygiene 23, 902–9.
Wilkins H. A., Goll P. H., Marshall T. F. de C. & Moore P. J. (1984). Dynamics of Schistosoma haematobium infection in a Gambian community. III. The acquisition and loss of infection. Transactions of the Royal Society of Tropical Medicine and Hygiene 78, 227–32.
Wong M. S., Bundy D. A. P. & Golden M. H. N. (1988). Quantitative assessment of geographic behaviour as a potential source of exposure to geohelminth infection. Transactions of the Royal Society of Tropical Medicine and Hygiene 82, 621–5.
Woolhouse M. E. J. (1992). A theoretical framework for the immunoepidemiology of human helminth infection. Parasite Immunology 14, 563–78.
Woolhouse M. E. J. & Chandiwana S. K. (1989). Spatial and temporal heterogeneity in the population dynamics of Bulinus globosus and Biomphalaria pfeifferi and in the epidemiology of their infection with schistosomes. Parasitology 98, 2134.
Woolhouse M. E. J., Ndamba J. & Bradley D. J. (1994). On the interpretation of intensity of infection data for Schistosoma haematobium. Transactions of the Royal Society of Tropical Medicine and Hygiene 88, 520–6.
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