Poisson approximations for epidemics with two levels of mixing. (Q1879880)

The authors consider rather general models of epidemic spread in heterogeneous populations, where individuals make random contacts both locally and, at a reduced rate, globally. They derive a sufficient condition under which the distribution of the number of individuals who survive the epidemic converges weakly to a Poisson distribution as the population size tends to infinity; see also \textit{H. E. Daniels} [Proc. 5\,th Berkeley Symp. Math. Stat. Probab. 4, 281--293 (1967)]. The result is specialized to a households model, to an overlapping groups model, and to the great circle model.