The divorce effect in the SIR model.
(a) Typical time-series showing the divorce effect. Beginning at time zero, a year-long 50% reduction in the transmission parameter of an endemic infection (R0 = 5, β = 365/year, γ = 73/year) reduces prevalence of the infection to near zero for the length of the control, where it remains until time 1.5 yrs, at which point a large post-control outbreak occurs. RCI falls towards zero as prevalence remains low, but the post-control outbreak is large enough to bring RCI well above 1 (peak RCI is approx. 1.4). (b) Magnitude of divorce effect in terms of relative cumulative incidence (RCI). Maximum RCI is found as the highest value of RCI observed within 25 yrs following a 100% effective control of an infection with 1<R0<20 and lasting between 1 month and 35 years. RCI>1 indicates the divorce effect and we see that the divorce effect occurs across a large portion of the parameter space, and ubiquitously for controls lasting less than 20 years. β is varied to attain the desired R0, all other parameters as in (a). (c) Maximum RCI for a given effectiveness and duration of control. The maximum RCI is found as the maximum observed RCI within 25 yrs after the end of a control that is between 0% and 100% effective and lasts between 1 month and 20 years (R0 = 5). The ridge between areas of high and low maximum RCI results from ineffective controls being maintained long enough for outbreaks due to the honeymoon effect deplenishing the population of susceptible individuals before the control periods end. All other parameters as in (a).