One of the main challenges in Bayesian design is approximating the expectation of a utility function which provides a measure of the information expected to be gained from an experiment. This is a particularly challenging task for many models in epidemiology as typically the likelihood is computationally intractable. In this talk, a synthetic likelihood approach is considered which allows the total entropy utility function to be used to derive designs for efficient parameter estimation and model discrimination. A number of experiments in epidemiology which are described by stochastic processes motivate this work. These processes include the Susceptible-Infected model and the Susceptible-Exposed-Infected model.