key: cord-1022650-i0udypkx
authors: Li, Guanlin; Shivam, Shashwat; Hochberg, Michael E.; Wardi, Yorai; Weitz, Joshua S.
title: Disease-dependent interaction policies to support health and economic outcomes during the COVID-19 epidemic
date: 2021-06-10
journal: iScience
DOI: 10.1016/j.isci.2021.102710
sha: 54a3887a204fac6d91a454219487eef8e0828c90
doc_id: 1022650
cord_uid: i0udypkx

Lockdowns and stay-at-home orders have partially mitigated the spread of Covid-19. However, en masse mitigation has come with substantial socioeconomic costs. In this paper we demonstrate how individualized policies based on disease status can reduce transmission risk while minimizing impacts on economic outcomes. We design feedback control policies informed by optimal control solutions to modulate interaction rates of individuals based on the epidemic state. We identify personalized interaction rates such that recovered/immune individuals elevate their interactions and susceptible individuals remain at home before returning to pre-lockdown levels. As we show, feedback control policies can yield similar population-wide infection rates to total shutdown but with significantly lower economic costs and with greater robustness to uncertainty compared to optimal control policies. 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.

while minimizing impacts on economic outcomes. We design feedback control policies informed 23 by optimal control solutions to modulate interaction rates of individuals based on the epidemic 24 state. We identify personalized interaction rates such that recovered/immune individuals elevate 25 their interactions and susceptible individuals remain at home before returning to pre-lockdown 26 levels. As we show, feedback control policies can yield similar population-wide infection rates to 27 total shutdown but with significantly lower economic costs and with greater robustness to 28 uncertainty compared to optimal control policies. Our analysis shows that test-driven 29 improvements in isolation efficiency of infectious individuals can inform disease-dependent 30 interaction policies that mitigate transmission while enhancing the return of individuals to pre-31 pandemic economic activity.

As of 7 March 2021, more than 116,166,652 cases of coronavirus disease 2019 (COVID-19) 37 have been reported worldwide with more than 2,582,528 deaths globally (WHO, 2021) . Starting Hence, distinct from lockdowns, there is an increasing interest in implementing population-wide 60 prevention methods that decrease transmission risk while enabling economic re-engagement. control strategies hinges on the accurate identification and isolation of exposed and infectious 79 cases. Intensive and stringent testing and isolation policies have even enabled some countries to 80 reopen (Coglianese and Mahboubi, 2021) . Slow return of test results (primarily) and false 81 negatives (as a secondary factor) limit the effectiveness of test-based control policy (Larremore 

Non-pharmaceutical COVID-19 control until effective vaccines become widely available will 94 necessarily involve periods of reduced social and economic activity; i.e., 'business, but not as 

Here we confront a joint problem: how to identify policies that aim to reduce fatalities arising 98 from COVID-19 while also enabling economic engagement. First, we use optimal control to 99 assess both health and economic outcomes in an SEIR disease model framework. There is a 100 substantial and growing literature on optimal control for COVID-19, the bulk of which focuses 101 on non-personalized release policies or policies that target age-or risk-stratified groups (Bonnans 2020; Zhao and Feng 2020). Here, we identify optimal control policies to modulate interaction 104 rates based on disease -unifying prior efforts centered on isolation and shield immunity. We find 105 that intermediate policy outcomes can do nearly as well as strict public health scenarios, without 106 incurring the severe costs as suppression-centered policies. However, optimal controls can be 107 fragile, when applied in practice given that they rely on time-rather than state-based Hence, guided by the optimal control analysis, we identify state-dependent policies similar to 110 feedback control that provide actionable guidance for individual behavior. As we show, using 

Optimal control framework for state-dependent contact rates policies that balance public 117 health and socioeconomic costs 118 We develop an optimal control framework to identify policies that address the tension between 119 decreasing contacts (that reduce new infections) with increasing contacts (that are linked to 120 socio-economic benefits). We represent the epidemic using a Susceptible-Exposed-Infectious- Figure 1 ). In doing so, the force of infection is influenced by state-specific 123 contact rates c S , c E , c I and c R for susceptible, exposed, infectious and recovered/immune 124 individuals, respectivelythese different levels form the basis for a control policy that directs 125 individuals to interact at different levels depending on their test status.

In the optimal control framework, a set of state-specific contact rates are identified that minimize 128 the appropriately weighted sum of what we term 'public health' and 'socioeconomic' costs.

Public health costs are quantified both by average infected levels and cumulative deaths.

Socioeconomic costs are quantified in terms of reductions in the total rate of interactions and by 131 shifts in state-specific contact rates. The optimal control 'solution' is then a time-dependent set 132 of disease-specific rates which are both shaped by and shape the epidemic itself (see SI/Methods 133 for details on the gradient projection algorithm used to identify the solution). Note that we 134 constrain the contact rate of exposed individuals to be equal to that of susceptible individuals 135 given the challenges of timely identification of exposed individuals who are not yet infectious 136 (and presumably have insufficient viral titer to be identified using screening tests; an issue we 137 return to in the Discussion). Finally, we utilize the parameter ξ to regulate the relative 138 importance of costs associated with death and spread of infection vs. socioeconomic impact. in the optimal control case are higher in the short-term but approach that of the baseline scenario 153 in the long-term. Indeed, the effective reproduction number identified via an optimal control 154 framework in the balanced scenario gradually reduces to sub-critical levels (close to an effective 155 reproduction number, ℛ eff = 0.75) while gradually relaxing controls over time. The optimal 156 control solutions are shown in Figure 2A . The optimal control solutions differ based on disease 157 status, recovered/immune individuals elevate their interactions, infectious individuals isolate, and 158 susceptible individuals lock-down before gradually returning to pre-lockdown levels.

Personalized, test-based optimal control policies and their impact on public health and 162 socioeconomic outcomes. 163 In order to explore the mechanisms identified by the optimal control framework, we 164 systematically modulate the effectiveness of isolation and evaluate its effect on the state-165 dependent optimal contact rates and disease dynamics. In practice, isolation effectiveness is First, in the low (25%) or medium (50%) effectiveness cases, susceptible, exposed, and 'epidemic age'. In order to evaluate the sensitivity of optimal control policies due to mis-timing, 198 we first computed the optimal control policy for a system one month after an outbreak. However, 199 instead of implementing the policy matched to the actual epidemic age, we enforce the optimal 200 control policy 30 days later, i.e. at the end of 60 days after the start of the outbreak. Figure S7   201 shows the difference in the mis-timed control policy vs. the optimal control policy; as is evident 202 the mistimed policy relaxes stringent lockdown when the optimal policy continues to lock-down.

As a consequence the total deaths are far higher for 25% and 50% isolation efficiency (see Table   204 1). The mistimed policy, in effect, biases the system towards minimizing socioeconomic rather 205 than public health costs. This significant difference in performance metrics demonstrates the 206 potential shortcomings of implementing a policy based on optimal control. However we note that 207 with a stringent isolation efficiency, delays are less problematic. The reason is that with efficient 208 infected case isolation, both the mis-timed and optimal control policy could enable nearly all 209 individuals to work, given that ℛ eff is held below 1 by infection isolation on its own.

Despite its fragility, we identify common features of the optimal control policy given variation in Critically, the performance of the test-driven feedback policy is nearly identical for the 254 performance metrics with or without mis-timing (see Table 2 ). This finding implies that state-255 based approaches will be less likely to have exponentially mis-timed applications, and reinforces 256 the need for population-scale testing for both active infections and recovered/immune individuals.

To examine the robustness of the feedback strategy in terms of model mis-specification, we 258 consider three cases in which the isolation efficiency is unbiased, overestimated (by ~10%) and 259 underestimated (by ~10%) relative to the true value. We then compare the total deaths and 260 working fraction of a feedback strategy based on these (potentially incorrect) estimates of the 261 J o u r n a l P r e -p r o o f isolation efficiency. We find that the feedback strategy is robust to such mis-specification, 262 particularly when isolation efficiency is high or low (see SI Figure S11 for details). We also note 263 that a simple policy with only two states -'lockdown' and 'open', respectively, corresponding to 264 minimum and baseline contact rates for the susceptible cases, would be easier to implement than 265 one with continuous 'phases' or state changes. In Figures S9 and S10 We have developed a linked series of optimal-and feedback-control analyses to evaluate the 277 effectiveness (and benefits) of modifying contact rates for managing the COVID19 pandemic test-driven, policies as the basis for mitigation that reduce risk for all.

Limitations of the study 314 The SEIR framework used as the basis for the present control study is intentionally simplified.

The epidemic model does not account for process or observational noise, analytic test features, 

A 408 serological assay to detect SARS-CoV-2 seroconversion in humans. medRxiv

Economic benefits of covid-19 411 screening tests (No. w28031)

Pandemic Planning in 416 Homeless Shelters: A pilot study of a COVID-19 testing and support program to mitigate 417 the risk of COVID-19 outbreaks in congregate settings

Optimal control techniques based on infection age for the study of the 420 COVID-19 epidemic

COVID-19 and Remote 423 Work: An Early Look at US Data

The role of 426 community-wide wearing of face mask for control of coronavirus disease 2019 (COVID-427 19) epidemic due to SARS-CoV-2

The effect of travel 429 restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak

Physical distancing, face 432 masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and 433 COVID-19: a systematic review and meta-analysis

Administrative Law in a Time of Crisis: Comparing 436 National Responses to COVID-19

Impact assessment of non-439 pharmaceutical interventions against coronavirus disease 2019 and influenza in Hong Kong: 440 an observational study

The Lancet Public Health

Implementation of a pooled surveillance testing program for asymptomatic 443 sars-cov-2 infections on a college campus-Duke university, durham, north carolina

Mitigating the wider health 447 effects of covid-19 pandemic response

Covid-19 -Navigating the Uncharted

Rational use of face masks in the COVID-451 19 pandemic

Impact 453 of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare 454 demand

CoV-2 transmission suggests epidemic control with digital contact tracing

Estimating the 461 effects of non-pharmaceutical interventions on COVID-19 in Europe

A feedback SIR (fSIR) model highlights advantages and limitations of infection-464 dependent mitigation strategies

Surveillance-to-diagnostic testing 467 program for asymptomatic SARS-CoV-2 infections on a large, urban campus-Georgia 468 institute of technology

Face masks for the public during 471 the covid-19 crisis

Temporal dynamics in viral shedding and 473 transmissibility of COVID-19

Importance of suppression and mitigation measures in managing COVID-19 476 outbreaks

The effect of large-scale 478 anti-contagion policies on the COVID-19 pandemic

Modeling serological testing to inform 480 relaxation of social distancing for COVID-19 control

The effect of 483 human mobility and control measures on the COVID-19 epidemic in China

Serology assays to manage COVID-19

Test sensitivity is 488 secondary to frequency and turnaround time for COVID-19 surveillance

Optimal, near-optimal, and robust epidemic control 491

Protecting the Population with Immune Individuals

COVID-19 Immunity Passports and Vaccination Certificates: Scientific

The case 499 for altruism in institutional diagnostic testing

The impact of 502 COVID-19 and strategies for mitigation and suppression in low-and middle-income 503 countries

Modeling 505 shield immunity to reduce COVID-19 epidemic spread

Awareness-driven behavior changes can shift the shape 507 of epidemics away from peaks and toward plateaus, shoulders, and oscillations

Proceedings of the National Academy of Sciences

Connecting clusters of 514 COVID-19: an epidemiological and serological investigation

Identifying airborne transmission as the 517 dominant route for the spread of COVID-19

Staggered release policies for COVID-19 control: Costs and benefits of relaxing 520 restrictions by age and risk

COVID-19 weekly epidemiological update

Flattening the unemployment curve policies to support workers' income and promote a speedy 523 labour market recovery

524 OECD 2020b

The territorial impact of COVID-19: Managing the crisis across levels of government

Infectious diseases of humans: dynamics and control

Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 538 2019 novel Coronavirus

Optimization: algorithms and consistent approximations

Optimal control theory: an introduction

Calculus of variations and optimal control theory: a concise introduction

Modeling shield immunity to reduce COVID-19 epidemic spread

A genetic algorithm tutorial

The MathWorks I (2020) Global Optimization Toolbox