Relatedness of the incidence decay with exponential adjustment (IDEA) model, “Farr's law” and SIR compartmental difference equation models

Santillana, Mauricio; Tuite, Ashleigh; Nasserie, Tahmina; Fine, Paul; Champredon, David; Chindelevitch, Leonid; Dushoff, Jonathan; Fisman, David

One of us (PF) had previously written about Farr's law and its importance in the development of epidemic theory (Fine, 1979) , and noted the conceptual similarity between IDEA and Farr's law. Upon exploration of these two approaches we realized that they, notwithstanding having been formulated some 160 years apart, and being based on very different theoretical constructs, are fully consistent with one another. Here we demonstrate the equivalence of these methods for epidemic modeling and forecasting, explore the potential advantages of using these methods to complement other approaches, and identify the circumstances under which these methods closely approximate the commonly-used SIR modeling approach. We explore numerical examples derived from recent emerging infectious diseases, including 2014e2015 West African Ebola virus outbreak. We show that these methods work fairly well in a number of cases, and discuss what this fact implies about difficult-to-measure components of transmission and control parameters.