Markov Chain Methods in Chain Binomial Epidemic Models

Abstract

In this paper, Markov chain methods are applied to chain binomial models in epidemics. In both Greenwood and Reed-Frost chain binomial models, it is shown that the susceptibles and susceptibles together with infectives respectively form Markov chains. These chains are used to obtain probabilities for the duration time and the total number of cases in an epidemic. A study of chain binomial models as Markov chains imbedded in continuous time processes is made. A practical application of the effects of inoculation on an epidemic is carried out, and some numerical results for the mean duration times and mean numbers of cases given.