How seasonal variations in birth and transmission rates impact population dynamics in a basic SIR model

Abstract

The changing climate is expected to alter the timings of key events in species life-histories. These shifts are likely to have important consequences for infectious disease dynamics, as the distribution and abundance of host species will lead to a different environment for parasites. Previous work has shown how seasonality in single host traits - most commonly the reproduction rate or transmission rate - can lead to an array of complex epidemiological dynamics, including chaos and multiple-stable states, with changes to the timing and amplitude of the seasonal peaks often driving drastic changes in behaviour. However, more than one life-history trait is likely to be seasonal, and changing environmental conditions may impact each of them in different ways, yet there have been few studies of host-parasite dynamics that include more than one seasonal trait. Here we examine a Susceptible-Infected-Recovered epidemiological model in which both reproduction and transmission exhibit seasonal fluctuations. We examine how the amplitude and timing of these seasonal peaks impact disease dynamics. We show that the relative timing of the two events is key, with the most stable dynamics when births peak a few months before transmission. We also show that chaotic dynamics become more likely when transmission in particular has a high amplitude, and when baseline transmission and virulence are high. Our results emphasise the importance of seasonality and timing of host life-history events to disease dynamics.