Optimal timing of one-shot interventions for epidemic control

Abstract

The interventions and outcomes in the ongoing COVID-19 pandemic are highly varied. The disease and the interventions both impose costs and harm on society. Some interventions with particularly high costs may only be implemented briefly. The design of optimal policy requires consideration of many intervention scenarios. In this paper we investigate the optimal timing of interventions that are not sustainable for a long period. Specifically, we look at at the impact of a single short-term non-repeated intervention (a “one-shot intervention”) on an epidemic and consider the impact of the intervention’s timing. To minimize the total number infected, the intervention should start close to the peak so that there is minimal rebound once the intervention is stopped. To minimise the peak prevalence, it should start earlier, leading to initial reduction and then having a rebound to the same prevalence as the pre-intervention peak rather than one very large peak. To delay infections as much as possible (as might be appropriate if we expect improved interventions or treatments to be developed), earlier interventions have clear benefit. In populations with distinct subgroups, synchronized interventions are less effective than targeting the interventions in each subcommunity separately.

Optimizing time-limited non-pharmaceutical interventions for COVID-19 outbreak control

“…This study adds to the current epidemiological modelling work [9][10][11][12][13][14] to explore the concept of NPI optimization. We identified an optimal parameter space for all considered intervention scenarios, with each scenario capable of minimizing both I max and I c (t max ) for a given set of optimal parameter values.…”

“…Intervention optimization has been proposed as a method to allow policymakers to fine-tune the characteristics of an intervention to minimize epidemiologically relevant outcome measures. Optimization has been explored for a range of potential COVID-19 NPI strategies, including single time-limited reductions to transmission [9,10], intermittent pulsing of NPIs [11,12] and gradual ramping-down of intervention measures following an initial reduction to transmission [12][13][14]. This has been explored in the context of minimizing the peak incidence or prevalence, analogous to 'flattening the curve' of an outbreak.…”

Minimizing the infected peak utilizing a single lockdown: a technical result regarding equal peaks

“…A constrained optimization problem is solved in [12], where the time minimal distancing policy which maintains an upper bounded on the infected population is derived. There are also a number of works which minimize the total number of infections during an epidemic during a period of such distancing; this is studied numerically in [9] and analytically in [13,14,15]. Interestingly, the main result of [13] is that the optimal lockdown policy to minimize the total number of infected individuals coincides with the protocol considered in this work; see equation ( 4) below.…”

“…Interestingly, the main result of [13] is that the optimal lockdown policy to minimize the total number of infected individuals coincides with the protocol considered in this work; see equation ( 4) below. However, as observed in [9], the timing with respect to these differing objectives (minimizing infected peak vs. minimizing total number of infections) in general do not agree, so that policy makers cannot generally hope to achieve both simultaneously. This work is organized as follows.…”

“…Again minimizing the infected peak, the authors of [8] determine the optimal (again, possibly complete) lockdown schedule as a feedback mechanism. Numerical results for a variety of epidemic objectives with respect to a single interval of distancing are provided in [9,10], and [11] studies the same problem both numerically and theoretically. A constrained optimization problem is solved in [12], where the time minimal distancing policy which maintains an upper bounded on the infected population is derived.…”