Epidemiological interactions between the local and the mean-field
by
Steven Webb
University of Strathclyde
Coauthors: Mike Boots (Sheffield University) Matt Keeling (Warwick University)

The assumption that populations are completely mixed is reasonable for many populations, but there is likely to be some degree of local interaction whether spatially or socially in many systems. An important question is therefore how strong these local interactions need to be before there are significant effects on the dynamics of the system. Our approach is to use correlation models, namely pair-wise models, to capture the spatial relationships of contacts and interactions between individuals. We first extend previous pairwise models to include immunity and reproduction from infecteds – dynamics that have been largely ignored in such systems. We then derive a multi-scale pair-approximation to move between completely local and completely mixed host-parasite interactions, thereby extending the reproduction processes of hosts and infection, and examine the long term effects of these differing spatial scales on the disease characteristics. Possible evolutionary traits of the pathogen within this multi-scale framework are then derived using adaptive dynamics.

Date received: May 15, 2008