Stein's method for epidemic processes (Q2707654)

This paper is concerned with a bound to the distance of the course in time of a general stochastic epidemic (GSE, not necessarily Markovian) over a finite time interval to its mean field limit. The procedure used to obtain this bound is Stein's method.NEWLINENEWLINENEWLINEThe author begins with a description of the GSE, reviewing the literature in the area. This is followed by an exposition of Stein's method, with several illustrative examples. The problem of the bound to the distance of the GSE from its mean field limit is then considered, and three theorems about it proved. The case of a Markovian epidemic provides an illustration, and a further theorem is then presented with the help of several lemmas.NEWLINENEWLINENEWLINEThe paper concludes with a discussion of the merits of Stein's method in an epidemic context. Graphs for the proportion of infectives and the cumulative infectivity function in Bartlett's GSE are sketched for three different sets of parameters. The references at the end of the paper run to 49 publications.NEWLINENEWLINEFor the entire collection see [Zbl 0948.00013].