With the global spread of COVID-19, compartmental epidemic models (such as SEIR models) have assumed an ever more important role in public health practice and planning. Even so, their implementation still necessitates a variety of practical compromises. Especially for stochastic Bayesian models, the computational complexity of fitting a straightforward state-space model grows quickly as the temporal and spatial dimension increases. In this talk, we’ll discuss the general properties of state-space models for infectious diseases and their importance in public health practice, and introduce several algorithmic approaches to obtain inferential results, including approximate Bayesian methods and MCMC strategies, focusing on their application to an analysis of cholera cases in Haiti and the Dominican Republic.