The impact of seasonal host reproduction on the population dynamics of host-macroparasite interactions is considered. We modify the classic Anderson and May model so that parameters associated with host reproduction are periodic functions of time with a period corresponding to a year. This allows us to compare our findings with those already well documented. If, in the absence of any seasonality, a stable steady-state solution exists annual reproduction gives rise to stable annual population cycles. Moreover, the parameter domain for which there is stability is increased by the seasonality. However, if the life span of the free-living stages is reasonably long, and the continuous model has limit cycle solutions, complex behavior can be observed in the seasonally forced case. Results also indicate that if seasonal effects are ignored, regulation of the hosts by the parasite population is overestimated.
White, K., Grenfell, B. T., Hendry, R. J., Lejeune, O., & Murray, J. D. (1996). Effect of seasonal host reproduction on host-macroparasite dynamics. Mathematical Biosciences, 137, 79-99. https://doi.org/10.1016/S0025-5564(96)00061-2