Disease dynamics in metapopulations

Structured populations are of particular interest when discussing disease dynamics. A common approach is to consider metapopulations: a group of coupled, well-mixed patches (also called (sub)populations or households). Two, frequently used ways to realize coupling are to introduce between-patch contact rates and to allow migration. Although these two ways describe different real-life situations, they result in similar dynamics under certain conditions. My project consists of two parts. In the first part, I focused on two different metapopulation models, both consisting of equally-sized, well-mixed, coupled patches. The first model consisted of subpopulations with standard SIR (susceptible-infected-recovered) dynamics, coupled by contact. In the second model, a latent period was introduces and patches were coupled by migration, but infectives were not allowed to migrate. For both of the models, stochastic individual-based models and the corresponding deterministic dynamics in the limit of an infinite number of (not necessarily large) patches were constructed and compared. The results imply equivalence for weak coupling. In the second part, I focus on the Tasmanian Devil Facial Tumour Disease (DFTD), an infectious cancer that threatens the species of tasmanian devils, the largest marsupial carnivore with extinction. I developed a stochastic, spatial, age-structured SEI model consisting of well-mixed patches with nearest neighbour interaction: migration and contact. I used parameter estimations from the literature, where available, and fit the rest of the parameters to published data. Results showed that migration was required for a healthy population to survive despite the strong demographic fluctuations and contact was needed to match the speed of the spatial spread. In the future, I will apply my model to make predictions and investigate possible control measures.