KaYin Leung: Dangerous connections: on binding site models for infectious disease dynamics

In this talk we formulate models for the spread of infection on dynamic networks that are amenable to analysis in the large population limit. We distinguish three different levels: (1) binding sites, (2) individuals, and (3) the population. In the tradition of Physiologically Structured Population Models, the model formulation starts on the individual level. Influences from the `outside world’ on an individual are captured by environmental variables. These environmental variables are population level quantities. A key characteristic of the network models is that individuals can be decomposed into a number of conditionally independent components: each individual has a fixed number of `binding sites’ for partners. The Markov chain dynamics of binding sites are described by a very low-dimensional system of ordinary differential equations. Yet we are able to characterize population-level epidemiological quantities, such as R0, r, and the endemic equilibrium, in terms of the corresponding variables. Moreover, individual-level probabilities are obtained from binding-site-level probabilities by combinatorics while population level quantities are obtained by averaging over individuals with respect to age.

(Joint work with Odo Diekmann)