Ball, Frank; Mollison, Denis; Scalia-Tomba, Gianpaolo Epidemics with two levels of mixing. (English) Zbl 0909.92028 Ann. Appl. Probab. 7, No. 1, 46-89 (1997). 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. Reviewer: J.M.Cushing (Tucson) Cited in 1 ReviewCited in 135 Documents 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.) Keywords:threshold conditions; local mixing; SIR epidemic PDFBibTeX XMLCite \textit{F. Ball} et al., Ann. Appl. Probab. 7, No. 1, 46--89 (1997; Zbl 0909.92028) Full Text: DOI