Bayesian inference of the basic reproduction number for a SIR epidemic model

Abstract

This paper is concerned with the Bayesian estimation for the basic reproduction number , defined as the expected number of new infectious from one infected individual in a fully susceptible population through the entire duration of the infectious period. This parameter is of great importance within epidemic modeling because no epidemic can occur if and an epidemic occurs if . Estimation of , or equivalent parameters in more complex models, can usually be achieved via Markov chain Monte Carlo (MCMC) methods. We will adopt the Bayesian method proposed by Eraker [MCMC analysis of diffusion models with application to finance. J Bus Econ Statist. 2001;19(2):177–191] in the context of financial models. The method consists of augmenting the low-frequency observations by the insertion of a finite number of latent data between two consecutive observations. We develop MCMC methods for inference to explore a posterior distribution of and of missing data. We illustrate the performance of the estimators on both synthetic data and real epidemic from the SIR (Susceptible-Infective-Removed) epidemic model and compare the results with the maximum likelihood (ML) method.