Small Worlds and Giant Epidemics

Monday, November 17, 2003 - 9:30am - 10:20am
Keller 3-180
Denis Mollison (Heriot-Watt University)
Key problems for models of disease spread relate to threshold, velocity of spread, final size and control. All of these depend crucially on the network structure of individual interactions.

Networks of interest range from the local extreme where interactions are only between nearest neighbours in some low dimensional space, and the infinite-dimensional 'mean-field' extreme where all interact equally with all. Intermediate cases of practical interest include 'small-world' and meta-population models.

I shall discuss the various structures of such models, their similarities and differences, and some approximations to them. The main aim is to identify what features of contact structure need to be captured when formulating a model for any specific problem of disease spread.