Speaker: Dr. Julien Arino, University of Manitoba
Title: Spread of infectious diseases in discrete space: metapopulation epidemic models
Abstract: There are a variety of ways to model the spatial and temporal spread of infectious agents. In the context of infectious pathogens of humans, several factors imply that it is often useful to consider space as consisting of a set of locations rather than as a continuous medium. Indeed, data collection and public health policy are typically carried out or determined at the jurisdictional level. One way to model spread in this context is to use so-called metapopulation epidemic models, in which a set of locations called patches are connected within a graph to describe the movement of individuals in this discrete space. Each vertex is endowed with a system describing the spread of disease in that location; coupling terms (often linear) then connect the "local" models. I will present the problem in one of the simplest possible settings, where spread in the vertices is modelled using ordinary differential equations (ODE). I will show how the behaviour of the resulting large systems of ODE can be studied using tools from both the theory of ODE and linear algebra. I will finish by discussing what are, in my view, interesting open issues in the area.