Modelling parasite density in ruminants

Models of parasite density in ruminants usually involve three nonlinear, coupled, ordinary differential equations for larval density, adult parasite density and host resistance. We deal with the inverse problem of objectively determining the nonlinear coefficients within the equations using available data. Experiments are suggested to allow efficient calculation of these coefficients. An alternative model is also proposed which reproduces key features of experimental results and shows the importance of including time delay equations in parasite modelling. References Anderson, R. M. and May, R. M. Herd immunity to helminth infection and implications for parasite control. Nature 315, 493--496, 1985. doi:10.1038/315493a0 Gordon, H. M. The epidemiology of parasitic diseases, with special reference to studies with nematode parasites of sheep. Australian Veterinary Journal 24, 17--45, 1948. doi:10.1111/j.1751-0813.1948.tb01569.x Hansen, J. and Perry, B. The epidemiology, diagnosis and control of helminth parasites of ruminants. International Laboratory for Research on Animal Diseases, 1994. Kao, R. R., Leathwick, D. M., Roberts, M. G. and Sutherland, I. A. Nematode parasites of sheep: a survey of epidemiological parameters and their application in a simple model. Parasitology 121, 85--103, 2000. http://journals.cambridge.org/action/displayIssue?jid=PAR&volumeId=121&issueId=01&iid=53786 Louie, K., Vlassoff, A. and Mackay, A. Nematode parasites of sheep: extension of a simple model to include host variability. Parasitology 130, 437--446, 2005. doi:10.1017/S003118200400678X Roberts, M. G. and Grenfell, B. T. 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, 1991. doi:10.1093/imammb/8.2.83 Roberts. M. G. and Heesterbeek, J. A. P. A simple parasite model with complicated dynamics. J. Math. Biol., 37: 272--290, 1998. doi:10.1007/s002850050129 Sargison, N. D, Wilson, D. J, Bartley, D. J, Penny, C. D and Jackson, F. Haemonchosis and teladosagiosis in a Scottish sheep flock putatively associated with the overwintering of hypobiotic fourth stage larvae, Veterinary Parasitology 147, 326--331, 2007. doi:10.1016/j.vetpar.2007.04.011 Vlassoff, A., Leathwick, D. M. and Heath, A. C. G. The epidemiology of nematode infections of sheep. New Zealand Veterinary Journal 49, 213--221, 2001. http://www.sciquest.org.nz/default.asp?pageid=69&pub=2&vol=49&iss=6 Waller, P. J., Dobson, R. J., Donald, A. D. and Thomas, R. J. Populations of strongylid nematode infective stages in sheep pastures: comparison between direct pasture sampling and tracer lambs as estimators of larval abundance. International Journal of Parasitology 11, 359--367, 1981. doi:10.1016/0020-7519(81)90006-