9. Stochastics

When fitting mechanistic models to data, we have to consider carefully the relationship between the nature of the data versus the nature of the model state variables. For example, when working with continuous-time S(E)IR models, it is important to keep in mind that incidence is not prevalence. The results from integrating the compartmental models represent prevalence over time (i.e., the number or fraction of a population that is infected). Most public health data, in contrast, tracks incidence—the number of new cases in any given time interval. We thus need to do something more than trying to match simulated prevalence with observed incidence. We therefore start with a toy example in which the simulated data actually represents prevalence.