The Effect of Seasonal Variation in Birth and Transmission Rates on Host-Parasite Relationships

Climate change is impacting ecosystems, and its effect on host-parasite systems is being noticed globally. With changing seasons comes changing species behaviour, and how these alternative behaviours might impact host-parasite systems is an important study area. Here we use and adapt classic susceptible-infected-recovered SIR compartmental disease models of hosts and parasites to consider how seasonality in both birth and transmission affect dynamics. We use the models to explore how seasonality drives behaviour of a population and its disease dynamics. We summarise how each seasonal component impacts population dynamics individually before incorporating both seasonal terms into the theoretical models. Simultaneous incorporation of seasonality in birth rate and seasonality in transmission leads to a wide range of population dynamics in each case where notably the timing of birth and transmission in relation to each other plays a pivotal role in determining the recurrence of disease cycles. The results obtained help us to understand, for example, how a host-parasite system might react after changing their behaviour due to a changing climate. We explore population management, or harvest, strategies with the aim of controlling the size of disease outbreaks without reducing population levels to critically low values. The timing of harvesting, in relation to the seasonal birth and transmission, is an important factor in determining the most appropriate disease control strategy. Overall, we show that the presence of seasonality in both birth and transmission plays a large role in determining population and disease dynamics, and that harvesting strategies can help to reduce disease whilst maintaining population size.