Seasonal forcing in a host-macroparasite system

Seasonal forcing represents a pervasive source of environmental variability in natural systems. Whilst it is reasonably well understood in interacting populations and host-microparasite systems, it has not been studied in detail for host-macroparasite systems. In this paper we analyse the effect of seasonal forcing in a general host-macroparasite system with explicit inclusion of the parasite larval stage and seasonal forcing applied to the birth rate of the host. We emphasise the importance of the period of the limit cycles in the unforced system on the resulting dynamics in the forced system. In particular, when subject to seasonal forcing host-macroparasite systems are capable of multi-year cycles, multiple solution behaviour, quasi-periodicity and chaos. The host-macroparasite systems show a larger potential for multiple solution behaviour and a wider range of periodic solutions compared to similar interacting population and microparasite systems. By examining the system for parameters that represent red grouse and the macroparasite nematode Trichostrongylus tenuis we highlight how seasonality could be an important factor in explaining the wide range of seemingly uncorrelated cycle periods observed in grouse abundance in England and Scotland.