We will be concerned with optimal intervention policies for a continuous-time stochastic SIR (susceptible - infective - removed) model for the spread of infection through a closed population. In previous work on such optimal policies, it is common to assume that model parameter values are known; in reality, uncertainty over parameter values exists. We shall consider the effect upon the optimal policy of changes in parameter estimates, and of explicitly taking into account parameter uncertainty via a Bayesian decision-theoretic framework. We consider policies allowing for (i) the isolation of any number of infectives, or (ii) the immunisation of all susceptibles (total immunisation). Numerical examples are given to illustrate our results.