title: A simple parasite model with complicated dynamics.
abstract: During their first year of life sheep acquire parasites through grazing, and simultaneously build up an immunity to infection. At the beginning of each year non-immune lambs are introduced onto contaminated pasture. We represent this process by differential equations describing the within-year dynamics, and defining a difference equation that describes the between-year dynamics. An example with two system parameters is analysed in detail. It is shown that regions exist in parameter space where periodic (between-year) or aperiodic solutions occur. Parasite control schemes could change the system dynamics from a stable equilibrium to complicated long-term fluctuations.
authors.affiliation: AgResearch, Animal Health Division, Wallaceville Animal Research Centre, Upper Hutt, New Zealand. robertsm@agresearch.cri.nz
authors.forename: M G
authors.initials: MG
authors.lastname: Roberts
authors.forename: J A
authors.initials: JA
authors.lastname: Heesterbeek
mesh_terms: D000818:Animals; D000829:Animals, Domestic; D000917:Antibody Formation / Q000502:physiology; D006790:Host-Parasite Interactions; D007411:Intestinal Diseases, Parasitic / Q000276:immunology / Q000469:parasitology / Q000662:veterinary*; D008954:Models, Biological; D009348:Nematoda / Q000254:growth & development / Q000276:immunology*; D009349:Nematode Infections / Q000276:immunology / Q000469:parasitology / Q000662:veterinary*; D009716:Numerical Analysis, Computer-Assisted; D012756:Sheep; D012757:Sheep Diseases / Q000453:epidemiology / Q000276:immunology / Q000469:parasitology*; D013997:Time Factors