Simple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).
Models incorporating at least one source of population-level variation (i.e., dispersion in either the transmission process or the observation process) provide reasonably good forecasts and parameter estimates, while models that incorporate only individual-level variation can lead to inaccurate (or overconfident) results. Models using continuous approximations to the transmission process showed improved computational efficiency without loss of accuracy.
Simple models of disease transmission and observation can be fitted reliably to simple simulations, as long as population-level variation is taken into account. Continuous approximations can improve computational efficiency using more advanced MCMC techniques.