Statistical models
Statistical models identify correlations between transmission drivers and outcomes and are typically stochastic in nature. However, they do not include dynamic processes. The predictive relationships are transparent; for example, an increase in factor N results in an X% increase in cases. They may incorporate temporal correlations such as time-series analysis in outcomes.
Statistical models are relatively easy to fit to data, with many existing software packages available for calibration. The results are straightforward to interpret and modeling approaches are well-understood by the modeling community. They do, however, struggle to incorporate heteroskedasticity; that is, if the spread of data points around the regression line is not uniform, they can result in misleading conclusions about the relationship between different variables.
Additionally, statistical models tend to overestimate transmission intensity since they tend to ignore depletions in the pool of susceptibles. They often fail to incorporate knock-on impact of interventions (for example, prevention of infection results in prevention of resulting secondary infections). Similar to compartmental models, statistical models make it difficult to incorporate complex interventions or realistic contact networks into a simulation.