Deterministic epidemic models overestimate the basic reproduction number of observed outbreaks

The basic reproduction number, R0, is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating this quantity from epidemic incidence data can lead to an over-estimation of this quantity. In particular, when fitting deterministic models to estimate the rate of spread, we do not account for the stochastic nature of epidemics and that, given the same system, some outbreaks may lead to epidemics and some may not. Typically, an observed epidemic that we wish to control is a major out- break. This amounts to implicit selection for major outbreaks which leads to the over-estimation problem. We show that by conditioning a ‘deterministic’ model on major outbreaks, we can more reliably estimate the basic reproduction number from an observed epidemic trajectory