Opportunities and challenges of Integral Projection Models for modelling host-parasite dynamics

Epidemiological dynamics are shaped by and may in turn shape host demography. These feedbacks can result in hard to predict patterns of disease incidence. Mathematical models that integrate infection and demography are consequently a key tool for informing expectations for disease burden and identifying effective measures for control. A major challenge is capturing the details of infection within individuals and quantifying their downstream impacts to understand population-scale outcomes. For example, parasite loads and antibody titres may vary over the course of an infection and contribute to differences in transmission at the scale of the population. To date, to capture these subtleties, models have mostly relied on complex mechanistic frameworks, discrete categorization and/or agent-based approaches. Integral Projection Models (IPMs) allow variance in individual trajectories of quantitative traits and their population-level outcomes to be captured in ways that directly reflect statistical models of trait-fate relationships. Given increasing data availability, and advances in modelling, there is considerable potential for extending this framework to traits of relevance for infectious disease dynamics. Here, we provide an overview of host and parasite natural history contexts where IPMs could strengthen inference of population dynamics, with examples of host species ranging from mice to sheep to humans, and parasites ranging from viruses to worms. We discuss models of both parasite and host traits, provide two case studies and conclude by reviewing potential for both ecological and evolutionary research.