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David , | cocooning pnn pAeiaAgain America Up Opening | oildistancing social a,1 c eateto nertv ilg,TeUiest fTxsa utn utn X78712; TX Austin, Austin, at Texas of University The Biology, Integrative of Department imr Singh Bismark , pnn pAmerica Up Opening | b hne Du Zhanwei , on doi:10.1073/pnas.2009033117/-/DCSupplemental ouaino 4,7 n oa ouaino ,6,1.Austin 2,168,316. of population total and high-risk a 547,474 Rock with of Austin), Austin–Round population (henceforth lifting Texas the of demonstrate, and in area enacting To metropolitan orders for distancing. shelter-in-place triggers social surveillance temporary of optimal derive relaxation we the guide to unmanageable avert disruption. economic to and social data, minimizing while hospitalization surges local hospital in trends based lockdowns on short-term enacting for guidance the frame- provides facing our work unintentionally, maker or policy intentionally a a either in scenario, For allow latter emerge. relaxation resources to a containment pandemic future, insufficient second rapidly other or to the distancing In social and a clusters. and tracing, costs emerging contact its contain testing, despite of distancing the up willing- social public future, ramping extreme of first sustain combination a the to through In ness bay at futures. held possible is unpredictable. policies two pandemic highly roughly distancing is which are social adherence, There future public on of depend impact burden will the The impor- reduce COVID-19. to incontrovertible populations of local vulnerable the sheltering exceed demonstrate of tance not we do while Finally, distancing hospitalizations social capacity. 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R.P., and B.S., D.P.M., D.D., contributions: Author owo orsodnemyb drse.Eal [email protected] Email: addressed. be may correspondence whom To ht os ooaiu akFret nomsrtge for strategies policies. inform distancing of to social Force state modulating to Task the the Coronavirus response and House Austin, Prevention, in and White of Control Disease been city for Centers has the the Texas, group, from work risk requests This group, of independent fidelity. age top with temporal on model and model simulation optimization SEIR-style mathematical surges. an a healthcare dis- develop overwhelming of We days preventing of while number local the ruption minimize monitoring can tem- by admissions States, triggered hospital United while orders the shelter-in-place waves across porary relaxed dis- pandemic social are COVID-19 future measures As tancing mitigate damage? economic best collateral limiting we can How Significance u piiainmdl ealdin detailed model, optimization Our we First, threefold. are article this of goals the end, this To c eyPasco Remy , PNAS e at eIsiue at e M87501 NM Fe, Santa Institute, Fe Santa b iceeMteais Friedrich-Alexander-Universit Mathematics, Discrete | uut1,2020 18, August d n arnAclMeyers Ancel Lauren and , raieCmosAtiuinLcne4.0 License Attribution Commons Creative | . y o.117 vol. https://www.pnas.org/lookup/suppl/ sdesigned is Appendix, SI | o 33 no. d Operations | 19873–19878 c,e at ¨

APPLIED BIOLOGICAL SCIENCES leadership enacted the Stay Home – Work Safe Order (SHWSO) the risks of the policy, indicated when the red (14) on March 24, 2020, requiring individuals to stay at home hospitalization curves surpass the red capacity line in Fig. 1. except for certain essential activities. The decision to do so was We first project COVID-19 hospitalizations in the extreme partially based on model projections provided by the Univer- scenario that the city maintains a 90% reduction in local sity of Texas at Austin. Three weeks later, a second order was transmission indefinitely through a combination of extensive issued, requiring cloth face coverings in public spaces. On May social distancing, transmission-reducing precautions, and proac- 1, 2020, Austin was forced to relax several of these requirements tive testing, contact tracing, and isolation (Fig. 1 A and B). and allow its citizens to return to work, entertainment, and com- The analysis assumes that schools remain closed, and cocooning merce as Texas mandated the first phase of Opening Up America of high-risk populations reduces their risk of by 95% Again (15). rather than 90%. Under this policy, we would not expect a second The analyses presented herein were requested by the Austin wave to emerge during the model horizon (Fig. 1A). Cumulative mayor and county judge and are informing ongoing risk assess- deaths would be expected to slowly climb to 81 (90% prediction ments, policy planning, and public messaging. We estimate that interval: 10 to 202). This scenario costs a year and a half (555 d) the COVID-19 began with a single importation case of . to Austin on February 15, 2020 and that the March 24 SHWSO In the other extreme, consider the scenario in which Austin reduced transmission by 95% through May 1, as fit using local permanently relaxes social distancing on May 1, while contin- hospitalization data; see SI Appendix. We project pandemic uing to cocoon high-risk populations and opening schools on hospitalizations under various intervention scenarios through August 18 (Fig. 1 C and D). While this policy requires a lock- September 2021. Schools are assumed to remain closed from down for only the initial 38-d period prior to May 1, we would March 14 until August 18, 2020. After that, they can be reopened expect a catastrophic surge in hospitalizations that exceeds the or closed in tandem with shelter-in-place orders (16). After May local capacity by 80% during July–September 2020, resulting in 1, we assume that the city is either in a relaxed state in which an expected 23,075 (90% prediction interval: 22,409 to 23,741) the transmission rate is partially but not fully reduced by lim- patients not receiving critical care. Without accounting for the ited measures and efforts to test, trace, and isolate cases, or a excess mortality during this period, which could be considerable, lockdown state in which renewed shelter-in-place orders reduce we would expect at least 30-fold higher COVID-19 mortality rel- transmission by 90% relative to the baseline. We find simple ative to the indefinite lockdown scenario, with deaths reaching triggers for issuing sheltering orders and estimate the impact of 2,957 (90% prediction interval: 2,868 to 3,040) by September cocooning vulnerable populations, that is, maintaining a 95% 2021. Under this policy, we expect two epidemic waves during reduction in transmission to high-risk individuals. These find- the model horizon, with the second large wave peaking in the ings provide actionable insights for other metropolitan areas late summer of 2020. where shelter-in-place orders have curbed the first wave of the Assuming that the first scenario is unattainable and the sec- COVID-19 pandemic. Moreover, the framework can incorpo- ond scenario unacceptable, we seek alternative policies that limit rate any dynamic model of COVID-19 transmission to support the number of days in lockdown while preventing COVID-19 similar planning throughout the . healthcare surges beyond local capacity. Based on our decision support efforts for the city of Austin and potential biases in Results confirmed case count data across the United States, we con- All of our results are based on simulating variable levels of jecture that local hospitalization data will be a more reliable social distancing using a data-driven model for COVID-19 trans- indicator of transmission intensity and future hospital surges. mission and healthcare needs in the Austin, TX, metropolitan Our best policies track daily COVID-19 hospital admissions and statistical area (MSA) (16). Based on COVID-19 hospitaliza- daily total hospitalizations across the city and trigger the initia- tion data from the Austin–Round Rock MSA through April 16, tion and relaxation of lockdown periods when admissions cross we estimate that local COVID-19 transmission rates dropped by predetermined thresholds. approximately 95% following the March 24 SHWSO, as detailed Specifically, we formulate and solve a stochastic optimization in SI Appendix. Our simulations assume that Austin maintained problem that selects daily hospitalization triggers and recom- this reduced transmission rate until the Texas governor issued mends reinstatement and relaxation of lockdown periods as the first statewide relaxation order, effective May 1 (17). Fol- follows: 1) reinstate the lockdown—corresponding to a 90% lowing that order, our model allows Austin to toggle between reduction in transmission—when the 7-d average of daily hospi- a relaxed state, in which transmission is reduced by 40% rela- tal admissions exceeds the trigger; and 2) release the lockdown— tive to the baseline transmission rate estimated prior to schools corresponding to a 40% reduction in transmission—when both a) closing on March 14, and a lockdown state, in which trans- the 7-d average of daily hospital admissions drops below the trig- mission is reduced by an estimated 90%. The relaxed state ger, and b) city-wide hospitalizations (heads in beds) are below a (40%) does not fully rebound to baseline transmission, under fixed factor (60%) of surge capacity for COVID-19. the assumption that testing-based containment and voluntary We include criterion 2b to hedge against premature relaxation social distancing will partially mitigate risks. The lockdown state when hospitals are relatively full. If randomized testing becomes does not quite reduce transmission as much as the original stay- available at sufficient scale, we could similarly determine triggers home order—by 90% rather than 95%—to account for likely based on testing rather than hospitalization data, and thereby declines in adherence. Further analyses for other degrees of gain earlier indications of a rising or declining threat. relaxation, ranging from a 20% to 80% reduction in transmission, Given the hospital capacity in the Austin, TX, metropolitan are provided in SI Appendix. All projections end in September area, we recommended a simple, yet robust, strategy with two 2021, which is an optimistic time horizon for the develop- fixed thresholds, as indicated by the blue step function in Fig. 1F. ment and distribution of prophylactic or therapeutic medical The policy tracks the 7-d moving average of daily COVID-19 countermeasures (18). hospital admissions and triggers the tightening and loosening To evaluate and optimize intervention policies, we compare of measures when the value crosses 80 daily admissions prior two outcome measures. First, we measure the total number to September 30, 2020, and 215 thereafter. We optimized these of days of lockdown (i.e., shelter-in-place) until September 30, two values as well as the date of the transition. Under the point 2021 as a proxy for the economic and societal costs of the pol- forecast for the pandemic, 135 d of lockdown are required, icy, depicted by gray shading in Fig. 1. Second, we determine and hospitalizations remain safely below capacity. Stochastic the probability of exceeding hospital capacity as a proxy for simulation yields a mean of 135 d (90% prediction interval: 126

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APPLIED BIOLOGICAL SCIENCES Table 1. Projected days of lockdown and COVID-19 mortality responding to future surges in hospitalizations—enact and then under the optimized strategies with 95% and 80% effective relax temporary lockdowns when daily hospital admissions climb cocooning of vulnerable populations above and eventually recede below a predetermined, optimized Scenario Cocooning at 95% Cocooning at 80% threshold. Whereas policy makers and public dashboards primar- ily track confirmed COVID-19 cases and deaths, we intentionally Days of lockdown use COVID-19 hospitalization data to fit our model parameters Mean 135 346 and guide policy. Hospitalization admissions are less subject to Median 135 347 bias than confirmed case counts, given the heterogeneous and 5 to 95% PI (126 to 141) (333 to 360) rapidly changing test availability and priorities across the United Cumulative deaths by States, and they are less time-lagged than reported COVID- September 30, 2021 19 deaths. Our policies are specifically designed to track a 7-d Mean 2,929 6,527 rolling average for daily COVID-19 hospital admissions, to pre- Median 2,646 6,532 vent overreacting to statistical variability and to account for 5 to 95% PI (2,837 to 3,026) (6,338 to 6,690) weekly periodicity in hospital reporting. The optimal strategies derived for Austin, TX, provide three The second and third columns correspond to Fig. 1 E and F and Fig. 1 G and H, respectively. Each 90% prediction interval (PI) (i.e., from 5 to 95%) critical insights. First, data-driven optimization yields policies shown in the table and in Fig. 1 is based on 300 simulations. that are expected to protect against catastrophic hospital surges while requiring far fewer days of costly shelter-in-place mea- sures than most sensible expert-designed strategies. For exam- to 141). The projected mortality is substantial, with a mean of ple, triggering lockdowns based on an arbitrarily chosen trigger 2,929 deaths (90% prediction interval: 2,837 to 3,026), which is of 50 new admissions per day should prevent hospitalizations again over 30 times larger than the baseline scenario of indefinite from reaching capacity, but they are expected to require more lockdown (Fig. 1A). While the other baseline scenario of indefi- than 150 additional days of lockdown, relative to the opti- nite relaxation projected similar COVID-19 mortality (Fig. 1C), mized trigger policy. However, implementing this trigger-based it produces a catastrophic surge in hospitalizations, and those optimization framework requires continual review of daily hos- projections do not account for excess mortality caused by inad- pital admissions and overall hospital utilization, as well as equate healthcare resources during the July–September 2020 constant validation of transmission rates during lockdown and surge period. relaxation phases. These projections assume an ambitious policy of cocooning Second, under the plausible scenario that transmission vulnerable populations with a 95% level of effectiveness. If rebounds to 60% of baseline (i.e., a 40% reduction), the best cocooning only attains an 80% reduction in transmission risk, strategy for limiting lockdowns without undermining the health- then we would expect far greater numbers of hospitalizations and care system would likely trigger only one future lockdown in deaths. Under this scenario, the optimal policy requires lower mid-June following a steep increase in hospitalizations that sur- thresholds for enacting lockdowns: a 7-d moving average exceed- passes the trigger of 80 new admissions per day (Fig. 1F). ing 30 daily COVID-19 hospital admissions prior to July 31, 2020 Hospitalizations would then be expected to peak and subside in and 110 thereafter (Fig. 1 G and H and Tables 1–3). Leaky late July, allowing relaxation of the lockdown by late September. cocooning can substantially undermine containment. In this case, The simultaneous release of the lockdown and start of a delayed the optimal strategy for managing hospital surge requires mul- 2020–2021 school year would fuel a third wave, which would be tiple periods of lockdown totaling about 350 d and more than expected to be self-limiting, that is, subside without requiring a doubling expected mortality. third lockdown period. This decline is driven by , We conducted sensitivity analyses to assess the robustness with an expected 79% of the population already infected and and limitations of the optimized triggers. The proposed triggers recovered by October 2021. are relatively robust to weaker social distancing during relax- We emphasize that, while this strategy offers a practical bal- ation periods, for example, if transmission is only reduced by ance between economic and healthcare constraints, it is not 20% rather than 40%. However, the proposed triggers are not designed to minimize morbidity and mortality and results in robust to leaky cocooning. We analyze the relative merits of poli- nearly 3,000 expected deaths by September 2021. If we assume cies with a constant lockdown threshold to the horizon, relative to having two distinct thresholds, as presented here. We show the importance of optimizing trigger thresholds: Conservative Table 2. COVID-19 mortality under the optimized strategies with triggers significantly increase the duration of lockdown periods, 95% and 80% effective cocooning of vulnerable populations while loose triggers result in hospital capacity being overrun. See SI Appendix for details. Percent deaths Risk group Age group Cocooning at 95% Cocooning at 80% Discussion A significant relaxation of social distancing in the absence of a Low risk comprehensive program for testing, contact tracing, and isola- 0 y to 4 y 0.03 0.02 tion will likely lead to future waves of the COVID-19 pandemic 5 y to 17 y 0.20 0.08 in US cities. Even if policy makers extend lockdown periods, lack 18 y to 49 y 9.01 3.60 of public willingness to comply might undermine their efficacy. 50 y to 64 y 18.23 6.97 Thus, planning for future relaxations is paramount to averting 65 y+ 4.43 6.12 unmanageable surges in COVID-19 hospitalizations. Carefully High risk designed strategies for triggering future shelter-in-place mea- 0 y to 4 y 0.00 0.02 sures can mitigate the impact on the community’s healthcare 5 y to 17 y 0.10 0.09 system while minimizing economic and societal costs. 18 y to 49 y 6.04 5.82 Our framework clarifies a key decision facing city and state 50 y to 64 y 26.86 28.32 leaders in the wake of the first wave of COVID-19—when 65 y+ 35.06 48.95 to enact and relax social distancing measures should the epi- The third and fourth columns correspond to Fig. 1 E and F and Fig. 1 G demic rebound. We posit a simple strategy for measuring and and H, respectively.

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COVID-19 city Executive Austin stay-home Austin’s the of full-blown allows city avoid that the example, to chart help For risk to States. five-stage method United a this the pan- adapted a the across have provide as cities we and policies in proof-of-concept COVID-19 unfolds a guiding demic relax- as for and serve framework lockdown to flexible of meant states is extreme It ation. two between toggle can enacted. are adherence accelerate cul- restrictions and to when responsibility leaders personal transitions city of sense extreme by a policies less tivate “track such multistage both of socialization of require proactive design that and the policies for trigger” advocate and also we buffers, in efruaea piiainmdlta eemnsdiyvle for values daily determines that model optimization an formulate We rela- a using optimization allow policies threshold simple Our city a which in scenario simple relatively a presents study Our PNAS | uut1,2020 18, August | o.117 vol. | o 33 no. 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APPLIED BIOLOGICAL SCIENCES optimization model has constraints that account for the epidemiological ity within the time horizon is, at most, 0.01. With these constraints in place, dynamics and a set of constraints that link that model’s 7-d moving average we select triggers to minimize the expected number of days of lockdown. of daily hospital admissions with the trigger thresholds, and the corre- Minimizing lockdown acknowledges social and economic pressures to relax sponding reductions in transmission via the contact matrices. A final set of stringent measures. constraints keep estimated hospitalizations within capacity. To do so, we All data required for this analysis can be found in SI Appendix. The code use the square-root staffing rule from queueing theory (22). This rule main- that produced the results of our analyses is available at https://github.com/ tains a high probability (we use ≥ 0.9999) that a single arrival in steady dukduque/COVID-TriggerOpt. state does not have to wait for service, and yet servers are highly utilized. Our “servers” are hospital beds, along with necessary healthcare providers ACKNOWLEDGMENTS. We thank the two anonymous referees for sugges- and equipment. We assume that 80% of Austin’s hospital beds are available tions and comments that improved the paper. This work was supported by the NIH under Grant NIH R01 AI151176, by Tito’s Handmade Vodka, and by for COVID-19 patients. We require that the square-root staffing rule hold, the US Department of Homeland Security under Grant 2017-ST-061-QA0001. under a point forecast for daily COVID-19 hospitalizations. In addition, we The views and conclusions contained in this document are those of the simulate, and optimize with respect to, 300 sample paths of the epidemic, authors and should not be interpreted as necessarily representing the offi- taking into account both macrolevel and microlevel stochastics, with details cial policies, either expressed or implied, of the US Department of Homeland in SI Appendix. We ensure that the probability of exceeding hospital capac- Security.

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