Maximum-likelihood estimation of the relative removal rate from the distribution of the total size of an intra-household epidemic

Abstract

In a previous paper (Bailey, 1953a) I discussed the distribution of the total size of a stochastic epidemic, involving both infection and removal, in a given group of homogeneously mixing susceptibles. The model employed was of the ‘continuous infection’ type, according to which infected individuals continue as sources of infection until removed from circulation by recovery, death or isolation. This may be contrasted with the chain-binomial type of model which entails short periods of high infectivity and approximately constant incubation periods (see, for example, Greenwood, 1931, 1949; Lidwell & Sommerville, 1951; Bailey, 1953b). The basic assumptions are that, with x susceptibles and y infectious persons in circulation, the chance of one new infection taking place in time dt is βxy dt, while the chance of a removal is γy dt, where β and γ are the infection and removal rates, respectively.