Foot and mouth disease is a highly contagious infectious disease which has frequently plagued many livestock across different countries worldwide. Currently the spread of the disease is not well understood, and thus experiments are needed such that targeted disease detection, prevention and control measures can be developed. However, developing such experiments is challenging as typically the likelihood for models for such infectious diseases is computationally intractable. This poses challenges in quantifying the usefulness of different experiments through a utility function. For this purpose, a synthetic likelihood approach is considered which allows experiments for infectious diseases to be developed through the consideration of important utility functions such as total entropy. This new methodology is applied to develop experiments for foot and mouth disease, and extensions to high dimensional design spaces are also considered.