The basic reproduction number, $R_{0}$, is probably the most important quantity in epidemiology. It is used to measure the transmission potential during the initial phase of an epidemic. This talk is concerned with the quantification of the spread of a disease modelled by a Markov chain. Due to the occurrence of repeated contacts taking place between a typical infective individual and other individuals already infected before, $R_{0}$ overestimates the average number of secondary infections. Two alternative measures, namely, the exact reproduction number, $R_{e0}$, and the population transmission number, $R_{p}$, are introduced to overcome this difficulty and provide valuable insight.

Stochastic epidemic; Basic Reproduction number; Disease Spread