9 - Stochastic analysis and disease transmission

Abstract

The formulation of various types of stochastic epidemic models is discussed, on the basis of well-known deterministic SIS and SIR epidemic models. Moreover, the three different types of stochastic model formulations are discussed, that is, the discrete time Markov chain (DTMC), the continuous time Markov chain, and the stochastic differential equations. The uniqueness of the properties that the stochastic (SDE) model holds is also investigated. We also discuss the DTMC formulations applicable in the study of epidemics within households (chain binomial models) and in the prediction of the initial spread of an epidemic (branching processes).