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 A, B, and C are constants. Of note, Brownlee's formulation identifies a process by which cases increase as a first order process, but decrease as a second order process, as is the case with the IDEA model. (Farr, 1840) . Black line, smallpox mortality by season; gray dots represent Farr's "model projections" derived by assuming a constant additive increase (approximately 5% per season) in the decline in smallpox deaths. Farr "smoothed" reported seasonal deaths by averaging adjacent seasons; hence model projections are plotted at the midpoint (e.g., "winterspring", "spring-summer") at each interval.