Estimation of the Basic Reproductive Number and Mean Serial Interval of a Novel Pathogen in a Small, Well-Observed Discrete Population

Background: Accurately assessing the transmissibility and serial interval of a novel human pathogen is public health priority so that the timing and required strength of interventions may be determined. Recent theoretical work has focused on making best use of data from the initial exponential phase of growth of incidence in large populations. Methods: We measured generational transmissibility by the basic reproductive number R0 and the serial interval by its mean Tg. First, we constructed a simulation algorithm for case data arising from a small population of known size with R0 and Tg also known. We then developed an inferential model for the likelihood of these case data as a function of R0 and Tg. The model was designed to capture a) any signal of the serial interval distribution in the initial stochastic phase b) the growth rate of the exponential phase and c) the unique combination of R0 and Tg that generates a specific shape of peak incidence when the susceptible portion of a small population is depleted. Findings: Extensive repeat simulation and parameter estimation revealed no bias in univariate estimates of either R0 and Tg. We were also able to simultaneously estimate both R0 and Tg. However, accurate final estimates could be obtained only much later in the outbreak. In particular, estimates of Tg were considerably less accurate in the bivariate case until the peak of incidence had passed. Conclusions: The basic reproductive number and mean serial interval can be estimated simultaneously in real time during an outbreak of an emerging pathogen. Repeated application of these methods to small scale outbreaks at the start of an epidemic would permit accurate estimates of key parameters.