The stochastic SEIR model before extinction: Computational approaches

•Efficient computational procedures are proposed for the stochastic SEIR epidemic model.•The ratio-of-expectations and the extinction time distributions are computed recursively.•The results are applied for the study of an outbreak of Marburg fever.

We study a stochastic epidemic model of Susceptible-Exposed-Infective-Removed (SEIR) type and we quantify its behavior during an outbreak. More specifically, we model the epidemic by a continuous-time Markov chain and we develop efficient computational procedures for the distribution of the duration of an outbreak. We also study the evolution of the epidemic before its extinction using the ratio-of-expectations (RE) distribution for the number of individuals in the various classes of the model. The obtained results are illustrated by numerical examples including an application to an outbreak of Marburg hemorrhagic fever.