where the pattern of secondary transmission follows a discrete probability distribution p k with k secondary transmissions. This approach accounts for demographic stochasticity, which can be crucial during the initial phase of an epidemic when the number of infected individuals is small. This has been applied to observed outbreak data for avian influenza, where extinction was observed before growing to a major epidemic [55] . Tiensin et al. [56] used flock-level mortality data and statistical back-calculation methods to estimate R 0 from an SIR model for the 2004 avian influenza epidemic in Thailand. They calculated R 0 to be between 2.26 and 2.64, depending on the length of the infectious period.