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

Chowell, Gerardo

Mechanistic models incorporate key physical laws or mechanisms involved in the dynamics of the problem under study (e.g., population or transmission dynamics) in order to explain patterns in the observed data. This type of models are often formulated in terms of a dynamical system describing the spatial-temporal evolution of a set of variables and are useful to evaluate the emergent behavior of the system across the relevant space of parameters (Brauer & Nohel, 2012; Chowell et al., 2016a; Strogatz, 2014) . In particular, compartmental models are based on systems of ordinary differential equations that focus on the dynamic progression of a population through different epidemiological states (Anderson & May 1991; Bailey, 1975; Brauer, 2006; Lee, Chowell, & Jung, 2016) . These models are useful to forecast prevalence levels in the short and long-term as well as assess the effects control interventions. In the context of disease transmission, population risk is typically modeled via a "transmission process" that requires contact between individuals or between an individual and external factors in the environment. Because the dynamic risk is limited to certain kinds of contact, the vast majority of epidemiological models divide the host population into different epidemiological states. Compartmental modeling allows researchers to address the conditions under which certain disease prevalence levels of interest will continue to grow in the population. Essentially this entails quantifying the factors that contribute to the "transmission" process. These models may be deterministic or stochastic, can incorporate geographic space, and can be structured by age, gender, ethnicity, or other risk groups (Sattenspiel, 2009 ). Such structuring is critical, since it defines discrete subgroups, or metapopulations, which may be considered networks wherein the populations are the nodes and their interconnections, the links.