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

The control of communicable diseases is an endeavor that has witnessed remarkable successes over the past century; diseases that previously caused large scale mortality have been eradicated (Hinman, 1999; Roeder, Mariner, & Kock, 2013) , locally eliminated (Papania et al., 2014) , or have been markedly reduced in incidence globally as a result of vaccination, antimicrobial therapy, water and sewage treatment, and advances in food safety (Armstrong, Conn, & Pinner, 1999; Liu et al., 2015; Murray et al., 2014) . Nonetheless, the threat of communicable diseases persists; emerging infectious diseases continue to be identified, often in association with changes in human and animal mobility, agricultural practices, environmental degradation, and misuse of antimicrobial therapy (Jones et al., 2008; Keesing et al., 2010; Kuehn, 2010) . Recent outbreaks or epidemics associated with MERS coronavirus (Azhar et al., 2014) , influenza A (H7N9) (Cowling et al., 2013) , and the West African emergence of the Zaire strain of Ebola virus (Baize et al., 2014) , have challenged epidemiologists as the natural history, modes of transmission, and/or means of control of these diseases have not been well understood during initial periods of emergence.