Suggested techniques for mitigating the divorce effect with seasonal transmission.
We consider an endemic disease, parameterized as in Fig 2(a). In all cases, twelve 1/12 yr. controls are used, to be consistent with the 1 yr. controls used in other figures, reducing the transmission parameter by 90% (ϵ = .9). (a) Pulsed control for seasonal SIR model. Control occurs yearly at a fixed time (when R0 is highest) for a fixed time (1/12 yr.) to control an endemic disease (parameterized as in Fig 2(a)). The control is effective at stopping the outbreak the first year, but seasonal outbreaks in subsequent years are larger, driven by an increasing population of susceptible individuals. Stopping the control program still results in a large post-control outbreak and a divorce effect. (b) Reactive control for Seasonal SIR. A fixed length (1/12 yr.) control is implemented to control an endemic disease (parameterized as in Fig 2(a)) once prevalence rises above a threshold (200 individuals in a population of 1 million). This stops the large early season outbreaks seen in the pulsed control, however the frequency of treatment increases as the susceptible population grows. Stopping the control program results in a large outbreak and divorce effect. (c) Informed control in seasonal SIR model. The first control period occurs at time 0. The beginning of the next control period is decided at the end of the previous control period, and is the day (allowed to be up to a maximum of 365 days later) that will result in the smallest divorce effect if control was stopped after that period. This plan finds that it is optimal to perform the first few treatments relatively quickly, then to perform subsequent treatments during the peak in prevalence. We see that this is capable of nearly eliminating the Divorce Effect, but there is only a minimal benefit to the control, with large yearly outbreaks.