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Epidemics with two levels of mixing. (English) Zbl 0909.92028
The authors develop a model for a SIR epidemic in which individuals mix at two levels: global and local. They investigate conditions under which an outbreak is possible and also the size of the outbreak. The main result is that local infectious contacts can have an amplification effect which can permit an outbreak to occur under conditions where a global homogeneous mixing model would not predict an outbreak. Threshold conditions are studied using branching approximations. They use their results to discuss vaccination strategies.

MSC:
92D30 Epidemiology
60K35 Interacting random processes; statistical mechanics type models; percolation theory
05C80 Random graphs (graph-theoretic aspects)
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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