The effects of seasonal forcing on invertebrate-disease interactions with immune priming

There is increasing experimental evidence that exposure to low doses of infection may 'prime' the immune response of invertebrate hosts, giving them greater protection against future infection. This form of immune memory is not compatible with the 'acquired immunity' modelled by the classic Susceptible-Infected-Recovered (SIR) epidemiological model, but instead requires the development of an alternative Susceptible-Primed-Infected (SPI) framework. Some initial theoretical work has explored the epidemiological and evolutionary dynamics of the SPI model, but these have assumed hosts exist in a constant environment. In reality, natural invertebrate-disease systems will be subject to significant environmental variation. Here, I use bifurcation analysis using numerical continuation software, complemented with numerical simulations, to investigate the effects of seasonal forcing on the already complex epidemiological dynamics of the SPI model. I show that multi-year cycles, quasi-periodicity, chaos, and multiple stability may all result, and highlight the importance not just of the forcing amplitude, but also the ecological and epidemiological background, for complex dynamics to emerge.