Timing social distancing to avert unmanageable COVID-19 hospital surges

Significance How can we best mitigate future pandemic waves while limiting collateral economic damage? As COVID-19 social distancing measures are relaxed across the United States, temporary shelter-in-place orders triggered by monitoring local hospital admissions can minimize the number of days of disruption while preventing overwhelming healthcare surges. We develop a mathematical optimization model on top of an SEIR-style simulation model with age group, risk group, and temporal fidelity. This work has been in response to independent requests from the city of Austin, the state of Texas, the Centers for Disease Control and Prevention, and the White House Coronavirus Task Force to inform strategies for modulating social distancing policies.

set of age groups {0-4y, 5-17y, 18-49y, 50-64y, 65y+} r ∈ R risk groups {low-risk, high-risk} Parameters Epidemiological parameters: β transmission rate σ rate at which exposed individuals become infectious τ proportion of exposed individuals who become symptomatic γA recovery rate from asymptomatic compartment γY recovery rate from symptomatic compartment γH recovery rate from hospitalized compartment η hospitalization rate after symptom onset Y HR a,r percent of symptomatic infectious that go to the hospital for a, r π a,r γY · Y HR a,r /[γY · Y HR a,r + η(1 − Y HR a,r )]: rate adjusted proportion for a, r µ rate from hospitalization to death; µ = γH in our instances HF R a percent of hospitalized that die for a, r ν a γH · HF R a /[γH · HF R a + µ(1 − HF R a )]: rate adjusted proportion for a, r φ a,r,t,high/low a ,r expected number of daily contacts from (a , r ) to (a, r) at t under high or low SD Na,r population of age-risk group a, r ω a,r The Xt toggle is determined by the thresholds lt and rt using the following logic: The systems from Eqs. [ and σ serves as the "success" probability. This construct is pervasive throughout right-hand side terms in Eqs. [1].

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In addition to these "micro" stochastics there are "macro" stochastics including modeling σ and γY and coupled 73 parameters as random variables; see Table S7  The trigger-based policy is closed-loop, i.e., adaptive, in the sense that the timing of lock-down and relaxation 102 depends on the sample path of the simulations. All results presented in the main text use 300 stochastic simulations 103 to compute the threshold policy, and an independent set of 300 out-of-sample simulations to report performance of 104 that policy. The initial conditions specify a single infectious individual. As a result, stochastic simulations sometimes 105 produce sample paths that quickly die out. In performing our Monte Carlo sampling, we reject samples that die 106 out since they are inconsistent with observed hospitalizations. Hence, we have to generate more than 300 total 107 sample paths to obtain 300 acceptable sample paths. We use a crude filter that simply requires at least 100 total 108 hospitalizations over the time horizon to September 2021. 109 We further investigated other classes of thresholds for the lock-down trigger, such as constant, linear, and quadratic  Tables S7 and S8 give numerical values and probability distributions for the epidemiological parameters and 118 hospitalization parameters that we use. Table S6 shows how overall age-risk group contact matrices are computed, as Tables S9-S12. After reporting additional analysis of trigger-based policies, the next section also details estimates of 122 age-risk populations.

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• Holidays and no school events are summarized in Table S13.

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Supplementary Analysis. We report additional results using the same format as the primary figure in the main text.
For easy reference, Figure S2a repeats the results for the optimized two-level trigger for the baseline analysis; i.e., we 163 assume 95% effective cocooning, and we toggle between 90% SD (lock-down) and 40% SD (relaxation). The daily 164 hospitalization thresholds, and the timing of the transition, are optimized using the model of Eq.
[4]. We fix the safety 165 trigger that prevents premature relaxation at 60% of hospital capacity. Part (b) of Figure S2 repeats this optimization, 166 but instead restricts solutions to a constant rather than two-level threshold. Parts (c) and (d) show the results of 167 stress tests, in which we assess the performance of the optimal strategies shown in parts (a) and (b) when relaxed 168 social distancing reduces transmission by only 20% rather than 40%. Under the two-level trigger, the point forecast 169 remains under hospital capacity but the distributional forecasts suggest a significant probability that hospitals will be 170 at, or just beyond, capacity at the peak in July. Under the constant trigger, even the point forecast "mildly" exceeds 171 hospital capacity.
172 Figure S3 performs an analogous stress test with respect to cocooning. First, we optimize for our baseline 90%-40% 173 SD toggle, under the assumption that cocooning is 95% effective (as in Figure S2a). Then, we evaluate the performance 174 under the assumption that cocooning is only 80% (rather than 95%) effective. Whereas our optimal policy is robust 175 to variation in the overall efficacy of social distancing ( Figure S2), it is highly sensitive to the efficacy of cocooning.

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This slight reduction in cocooning is expected to lead to catastrophic surges in hospitalizations, with capacity grossly 177 exceeded in the summer and early fall of 2020. This reinforces one of our primary conclusions, that vigilant cocooning 178 of vulnerable populations will be critical to preventing overwhelming healthcare surges and saving lives.

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To quantify the benefit of deriving optimal triggers versus sensible expert-designed strategies, we consider two 180 reasonable constant thresholds for initiating and relaxing social distancing. Part (a) of Figure S4 projects pandemic 181 waves and lock-down periods based on an arbitrary threshold that is below the optimal constant threshold shown in 182 Figure S2c and Part (b) similarly considers an arbitrary threshold above the optimal value.

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Finally, we consider a scenario in which transmission is more effectively mitigated during relaxation of social 184 distancing. When lock-downs are lifted, the population continues to reduce transmission by 80% rather than 40%.
185 Figure S5 projects COVID-19 under a policy that has been optimized under this more optimistic scenario. The model 186 projects that hospitalizations will remain under capacity without requiring another lock-down before September 2021 187 because of the stringent mitigation even during the relaxation period.
188 Table S1 is the analog of Tables 1-3    respectively. However, they assume that the public adheres only to 20% social distancing rather than the 40% for which the policy was designed. Hospital capacity may be exceeded if transmission rates are higher than expected during periods of relaxation. In all graphs, solid curves correspond to the point forecast and shaded regions give 90% prediction intervals based on 300 stochastic simulations. To make these graphs, we first derived the optimal thresholds for the baseline scenario which toggles between 90% (lock-down) and 40% (relaxation) transmission reduction, while assuming that cocooning remains 95% effective. Then, we evaluate performance of the triggering policy under the assumption that cocooning is only 80% effective in reducing infection risk in vulnerable populations. Imperfect cocooning is projected to result in catastrophic health care surges and more than double the mortality. In both graphs, solid curves correspond to the point forecast and shaded regions give 90% prediction intervals based on 300 stochastic simulations.   Table S1. Figure 1(a) and 1(b) Table S5. Projected days of lock-down, probabilities of exceeding hospital capacity and COVID-19 mortality under two scenarios. The first is a stress test, which optimizes assuming cocooning is 95% effective, but tests when it is instead 80% effective; this corresponds to Figure S3. The second policy corresponds to relaxed social distancing corresponding to 80% (rather than our nominal 40%) reduction in transmission under cocooning, which is 95% effective. In this case we do not need to enforce a lockdown after May 1, 2020 to prevent hospitalizations from exceeding capacity. The right-most column corresponds to Figure S5.

Projected days of lock-down, probabilities of exceeding hospital capacity and COVID-19 mortality under the indefinite lock-down and indefinite relaxation. Companion of
Age-stratified proportion of population at high-risk for COVID-19 complications: 195 We estimate age-specific proportions of the population at high risk of complications from COVID-19 based on data 196 for Austin, TX and Round-Rock, TX from the CDC's 500 cities project ( Figure S6) (6). We assume that high risk High-risk proportions for adults:

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To estimate the proportion of adults at high risk for complications, we use the CDC's 500 cities data mentioned above, 204 as well as data on the prevalence of HIV/AIDS, obesity and pregnancy among adults (Table S14).

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The CDC 500 cities dataset includes the prevalence of each condition on its own, rather than the prevalence of 206 multiple conditions (e.g., dyads or triads). Thus, we use separate co-morbidity estimates to determine overlap. The    Estimates provided by each of the region's hospital systems and aggregated by regional public health leaders