Abstract
This paper is concerned with a well-known epidemiological concept to measure the spread of infectious disease, that is, the basic reproduction number. This paper has two major objectives. The first is to examine Bayesian sensitivity and consistency of this measure for the case of Markov epidemic models. The second is to assess the Martingale method by comparing its performance to that of Markov Chain Monte Carlo (MCMC) methods in terms of estimating this parameter and the infection and removal rate parameters given only removal data. We specifically consider the Markovian SIR (Susceptible-Infective-Removed) epidemic model routinely employed in the literature with exponentially distributed infectious periods. For illustration, numerical simulation studies are performed. Abakaliki smallpox data are examined as a real data application.