Mathematical models in eco-epidemiology

• Main Author: Bate, Andrew M.
• Other Authors: Hilker, Frank
• Published: University of Bath 2014
• Subjects: 614.4
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616875

Diseases have the capacity to not only influence the dynamics of their hosts, but also interacting species like predators, prey and competitors. Likewise, interacting species can influence disease dynamics by altering the host's dynamics. The combination of these two effects is often called eco-epidemiology, the interaction of ecology and epidemiology. In this thesis, we explore this interplay of infectious diseases and predator--prey interactions, where the predator is a specialist. We start with an introductory chapter on modelling eco-epidemiology, with a particular focus on the myriad of different possible assumptions mathematical models in eco-epidemiology can have. In Chapter 2, we consider the effect predator--prey oscillations have on the endemic criteria for an infectious disease. In Chapter 3, we find a great variety of complex dynamics like tristability between endemic and disease-free states, quasi-periodic dynamics and chaos in a predator--prey model with an infectious disease in the predator. In Chapter 4, we consider the impact an infectious disease has on a group defending prey. Here, we find that the disease not only can coexist with a predator, it can actually help the predator survive where it could not in the absence of the disease, in stark contradiction to the principle of competitive exclusion which states that two exploiters should not coexist on a single resource. Lastly, in Chapter 5, we consider a spatial predator--prey model with a disease in the prey and focus on how preytaxis (the movement of predators along prey gradients) can alter various invasion scenarios. Through all these chapters, there is a common focus on the impact (endogenous) oscillations have in eco-epidemiology.