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

where t is an integer "generation" of an outbreak (thus t ¼ f1; 2; 3;…g2ℕ). In other words, in the IDEA model, the unit of time is the generation interval (the time interval between the time when an individual is infected by an infector and the time when this infector was infected). In Farr's model, t is the time at which subsequent observation are made. The parameter R 0 is the basic reproduction number as usually defined; that is, the number of secondary cases created by a primary case in a totally susceptible population and in the absence of intervention. The parameter d > 0 which we have referred to as a "control parameter" defines the rate at which transmission declines over the course of an epidemic. The empirical underpinnings of d are not yet well defined, but based on current understanding of disease dynamics could represent public health interventions, population adaptation or behavior change, improved availability of personal protective items or effect of drugs to treat infection, or reductions in population susceptibility as a result of immunity or vaccination. As noted above, by fitting the model to data we have previously obtained reasonable estimates of R 0 early in the course of epidemics, and have also been able to produce plausible near-term projections of future case counts.