A SIMPLE PARASITE MODEL WITH COMPLICATED DYNAMICS

During their first year of life sheep acquire parasites through grazin g, and simultaneously build up an immunity to infection. Al the beginn ing of each year non-immune lambs are introduced onto contaminated pas ture. We represent this process by differential equations describing t he within-year dynamics, and defining a difference equation that descr ibes the between-year dynamics. An example with two system parameters is analysed in detail. It is shown that regions exist in parameter spa ce where periodic (between-year) or aperiodic solutions occur. Parasit e control schemes could change the system dynamics from a stable equil ibrium to complicated long-term fluctuations.