This paper demonstrates that a simple stochastic model can capture the features of an epidemic of equine influenza in unvaccinated horses. When the model is modified to consider vaccinated horses, we find that vaccination dramatically reduces the incidence and size of epidemics. Although occasional larger outbreaks can still occur, these are exceptional. We then look at the effects of vaccination on a yard of horses, and in particular at the relationship between pre-challenge antibody level and quantity of virus shed when challenged with the virus. While on average, a high antibody level implies that less virus will be shed during the infectious period, we identify a high degree of heterogeneity in the response of horses with similar pre-challenge antibody levels. We develop a modified model that incorporates some heterogeneity in levels of infectivity, and compare this with the simpler model.