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

Furthermore, we noted that in the Chikungunya time series there was a large perturbation in best-fit values of d occurring in October 2014, corresponding with an apparent multi-wave epidemic. We have previously noted that this abrupt change in the generation-to-generation best fit value of d corresponds with the occurrence of multiwave epidemics when IDEA is fit to simulated data (Fisman et al., 2013) ; using Farr's approach, the onset of a possible new Chikungunya wave seems to correspond with an abrupt increase in K to a value far greater than one (Fig. 7) . The utility of large values of K as a signal of an incipient epidemic wave warrants further investigation. Fig. 2 . Relationship between the three models. Parameter r represent the relative risk of infection in each generation for the SIR model. The control parameter d is associated with the IDEA model and K is Farr's ratio. Fig. 3 . A heat map plotting values for R 0;SIR and r where the damped SIR model can be approximated by a IDEA model using equations (11) and (12). Darker areas indicate a good match (measured as the sum of squared differences) between the simulated incidence time series; lighter areas represent combinations of values for which incidence time series for SIR and IDEA diverge.