Estimating the basic reproduction number from surveillance data on past epidemics

• New synthetic stochastic model for an epidemic, incorporates deterministic SIR.
• Basic reproduction number: new estimators adapted to large population surveillance.
• Study in depth of the estimators: asymptotic properties and simulation studies.
• Practical issues: illustration on CDC data, comments on limitations and extensions.

In this paper, we consider the basic reproduction number, R0R0, a parameter that characterizes the transmission potential of an epidemic, and explore a novel way for estimating it. We introduce a stochastic process which takes as starting points the classical SIR (susceptibles-infected-removed) models, deterministic and stochastic. The estimation method rests on an extremum property of the deterministic SIR model, and could be applied to past surveillance data on epidemic outbreaks, data gathered at different locations or in different years. Our estimators take into account some practical limitations, in particular the fact that data are collected at preassigned times. We derive asymptotic properties of the estimators and perform a simulation study to assess their small sample behavior. We illustrate the method on real data (from the USA Centers for Disease Control and Prevention site) and we point to various extensions to our approach, as well as practical implementation issues.