Disease-dependent interaction policies to support health and economic outcomes during the COVID-19 epidemic

Abstract

Lockdowns and stay-at-home orders have partially mitigated the spread of Covid-19. However, the indiscriminate nature of mitigation - applying to all individuals irrespective of disease status - has come with substantial socioeconomic costs. Here, we explore how to leverage the increasing reliability and scale of both molecular and serological tests to balance transmission risks with economic costs involved in responding to Covid-19 epidemics. First, we introduce an optimal control approach that identifies personalized interaction rates according to an individual's test status; such that infected individuals isolate, recovered individuals can elevate their interactions, and activity of susceptible individuals varies over time. Critically, the extent to which susceptible individuals can return to work depends strongly on isolation efficiency. As we show, optimal control policies can yield mitigation policies with similar infection rates to total shutdown but lower socioeconomic costs. However, optimal control policies can be fragile given mis-specification of parameters or mis-estimation of the current disease state. Hence, we leverage insights from the optimal control solutions and propose a feedback control approach based on monitoring of the epidemic state. We utilize genetic algorithms to identify a 'switching' policy such that susceptible individuals (both PCR and serological test negative) return to work after lockdowns insofar as recovered fraction is much higher than the circulating infected prevalence. This feedback control policy exhibits similar performance results to optimal control, but with greater robustness to uncertainty. Overall, our analysis shows that test-driven improvements in isolation efficiency of infectious individuals can inform disease-dependent interaction policies that mitigate transmission while enhancing the return of individuals to pre-pandemic economic activity.

Figure 1:. Epidemic dynamics with optimal and feedback control of disease-status driven contact rates.

(Top) SEIR model schematic in which the force of infection is modulated by state-specific contact rates, see text and SI for details. (Middle) Diagram of optimal control approach: contact rates are pre-specified given model structure and estimate of parameters and current conditions. (Bottom) Diagram of feedback control approach: contact rates are updated in real-time based on measurements of the infected and recovered case counts via testing surveillance.

Figure 2:

Comparison of health and economic outcomes of COVID-19 given various interventions: baseline interactions (i.e., no intervention); optimal contact rate intervention (balance both health and economic outcomes) and fully lock down intervention (applied to all the subpopulations) with 75% isolation efficiency. (A) The optimal contact rate with 50% isolation effectiveness and shield immunity level 2. (B) Cumulative deaths (health outcome) during the epidemic. (C) Socio-economic costs (economic outcome) during the epidemic. (D) Measure of effective reproduction number (${\mathcal{R}}_{eff}$) for different interventions during the epidemic.

Figure 3:

SEIR dynamics with contact rate interventions for various isolation efficiencies, (A) 25% isolation efficiency; (B) 50% isolation efficiency and (C) 75% isolation efficiency. The relative importance (ξ) is 1 for all the cases (A), (B) and (C). The contact rate interventions start at 60 days, people follow baseline (or normal) interactions before that. For all the isolation efficiency scenarios (three rows), the left panel shows the population dynamics given the optimal contact rate shown in the middle panel. The gray curve in the middle panel represents the measure of corresponding effective reproduction number (${\mathcal{R}}_{eff}$). The right panel shows the corresponding socio-economic costs. See SI/Methods for additional scenarios.

Figure 4:

Heuristic state feedback intervention policies varying with isolation efficiency: (A) 25% isolation efficiency; (B) 50% isolation efficiency and (C) 75% isolation efficiency. The shielding levels considered here are 2 and 5 times the base contact rate (i.e., 200% shielding and 500% shielding respectively). An optimal line divides the plane into two regions which determines the optimal contact rate for the susceptible population for the current infected and recovered cases. The optimal policy in the dark grey region is lockdown for both shielding levels while the system with a higher level of shielding (level of 5) is open in the light grey region. The phase plots (red and blue curves) show the evolution of the infected and recovered case fractions over the period of 360 days, while applying the control strategy described above for shielding levels of 2 and 5 respectively. See SI/Methods for a larger set of plots with increments of 5% in isolation efficiency and for shielding levels of 2, 3, 4 and 5. The second and third plots show the infected and recovered cases for shielding levels of 2 and 5 respectively as functions of time. The vertical lines mark the time instances at which the policy is implemented with lockdown imposed and also the time at which it is lifted. For the case of isolation efficiency of 75%, no lockdown is needed at all for the susceptible population.