The stochastic general epidemic model revisited and a generalization.

While the mathematical theory of epidemics has its origins with Ross (1911), it was not until Kryscio (1975) that explicit expressions for the state probabilities of the classical general epidemic model established by Bartlett (1949) were found. However, these formulae were of limited practical use when the population size was of even moderate size. By shifting the focus from the bivariate pair representing the number of susceptibles and infectives to that for the number of infectives and removals, one is able to obtain solutions that are considerably simpler and easier to manage than those previously derived and which are not restricted by the size of the population. The results are obtained for a generalized general epidemic process in which transition probabilities are arbitrary functions of the state space, and then applied to the classical model. An extension to time-dependent transition rates is also considered.