Stochastic epidemics: the expected duration of the endemic period in higher dimensional models

A method is presented to approximate the long-term stochastic dynamics of an epidemic modelled by state variables denoting the various classes of the population such as in SIR and SEIR model. The modelling includes epidemics in populations at different locations with migration between these populations. A logistic stochastic process for the total infectious population is formulated; it fits the long-term stochastic behaviour of the total infectious population in the full model. A good approximation is obtained if only the dynamics near the equilibria is fit.