The population dynamics of nematode infections of ruminants: the effect of seasonality in the free-living stages.

A previously published differential equation model for the dynamics of nematode infections of ruminants is modified to allow for time-dependent development and loss rates in the free-living stages. This converts the nonlinear autonomous system to one with periodic coefficients. Fourier transform methods are used to analyse the response of the modified system to these forced oscillations. For biologically reasonable parameter values, the annual pattern of parasitism is determined for the nonautonomous system, and compared with that for the autonomous system with periodic perturbations, and a system incorporating both effects. It is found that, whereas periodic perturbations due to management intervention determine the qualitative annual patterns of larval abundance and host infection, the seasonal dynamics of the larval stages change the magnitude of the adult worm burden.