This paper is concerned with the Bayesian inference for the dependent parameters of stochastic SIR epidemic model in a closed population. The estimation framework involves the introduction of m − 1 latent data between every pair of observations. Kibble’s bivariate gamma distribution is considered as a good candidate prior density of parameters, they give an appropriate frame to model the dependence between the parameters. A Markov chain Monte Carlo methods are then used to sample the posterior distribution of the model parameters. Simulated datasets are used to illustrate the proposed methodology.