Estimating the basic reproductive number during the early stages of an emerging epidemic.

A novel outbreak will generally not be detected until such a time that it has become established. When such an outbreak is detected, public health officials must determine the potential of the outbreak, for which the basic reproductive numberR0 is an important factor. However, it is often the case that the resulting estimate of R0 is positively-biased for a number of reasons. One commonly overlooked reason is that the outbreak was not detected until such a time that it had become established, and therefore did not experience initial fade out. We propose a method which accounts for this bias by conditioning the underlying epidemic model on becoming established and demonstrate that this approach leads to a less-biased estimate of R0 during the early stages of an outbreak. We also present a computationally-efficient approximation scheme which is suitable for large data sets in which the number of notified cases is large. This methodology is applied to an outbreak of pandemic influenza in Western Australia, recorded in 2009.

Hybrid Markov chain models of S-I-R disease dynamics.

Deterministic epidemic models are attractive due to their compact nature, allowing substantial complexity with computational efficiency. This partly explains their dominance in epidemic modelling. However, the small numbers of infectious individuals at early and late stages of an epidemic, in combination with the stochastic nature of transmission and recovery events, are critically important to understanding disease dynamics. This motivates the use of a stochastic model, with continuous-time Markov chains being a popular choice. Unfortunately, even the simplest Markovian S-I-R model-the so-called general stochastic epidemic-has a state space of order [Formula: see text], where N is the number of individuals in the population, and hence computational limits are quickly reached. Here we introduce a hybrid Markov chain epidemic model, which maintains the stochastic and discrete dynamics of the Markov chain in regions of the state space where they are of most importance, and uses an approximate model-namely a deterministic or a diffusion model-in the remainder of the state space. We discuss the evaluation, efficiency and accuracy of this hybrid model when approximating the distribution of the duration of the epidemic and the distribution of the final size of the epidemic. We demonstrate that the computational complexity is [Formula: see text] and that under suitable conditions our approximations are highly accurate.