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

We recently proposed a descriptive approach to the initial estimation of the basic reproduction number ðR 0 Þ of an emerging or re-emerging pathogen, which also provides information on the rate at which the process is being controlled, as well as reasonable short-term projections of incidence. This two-parameter model, which we have referred to as the "Incidence Decay with Exponential Adjustment" (IDEA) model, offers advantages of simplicity, explicit linkage to theory of epidemic growth, and also acknowledges the fact that epidemics and outbreaks do not peak and end simply due to depletion of susceptibles, but because of a complex constellation of public health actions and behavioral changes that may modify the course of an epidemic and reduce the effective reproduction number R e ðtÞ during an outbreak (Fisman et al., 2013) . In our previously published description of this model, we validated model projections by showing that they were identical to those derived from a discrete-time susceptible-infectious-removed (SIR) compartmental model, provided the SIR model had a low basic reproduction number ðR 0 Þ and exponential improvement in control over the course of the epidemic (Fisman et al., 2013) .