Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts

Chowell, Gerardo

Mathematical models provide a quantitative framework with which scientists can assess hypotheses on the potential underlying mechanisms that explain patterns in the observed data at different spatial and temporal scales. Models vary in their complexity in terms of the number of variables and parameters that characterize the dynamic states of the system, in their spatial and temporal resolution (e.g., discrete vs. continuous time), and in their design (e.g., deterministic or stochastic). While agent-based models, formulated in terms of characteristics and interactions among individual agents, have become increasingly used to model detailed processes often occurring at multiple scales (e.g., within host vs. population level), models based on systems of ordinary differential equations are widely used in the biological and social sciences. These dynamic models are specified by a set of equations and their parameters that together quantify the spatial-temporal states of the system via a set of interrelated dynamic quantities (e.g, viral load, susceptibility levels, disease prevalence) (Banks et al., 2009) .