From Node to Network: Weaving A Global Perspective on Efficacy and Costs of Non-Pharmaceutical Interventions

From Node to Network: Weaving A Global Perspective on Efficacy and Costs of Non-Pharmaceutical Interventions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article From Node to Network: Weaving A Global Perspective on Efficacy and Costs of Non-Pharmaceutical Interventions Chong Xu, Sameer Kumar, Muer Yang, Nidhi Ghildayal, Charu Chandra This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4511189/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Jan, 2025 Read the published version in Scientific Reports → Version 1 posted 11 You are reading this latest preprint version Abstract Non-pharmaceutical intervention (NPI) policies, ranging from mild intervention to total isolation, were implemented during the COVID-19 pandemic across the globe. We adopt a systematic approach to guide policymakers in deployment of NPI policies to mitigate the pandemic's effects while maintaining a proper balance on their social and economic impacts. The optimal timings to enact and to end a policy depend both on the strictness of the policy and the transmissibility of the virus. Our results show that the strict policy is not always the most effective to mitigate the disease, while other modest NPIs can function better especially when the virus is highly transmissible. If an NPI can only be applied for a limited period due to economic and social constraints, it is always suboptimal to implement it at the pandemic's onset. Health sciences/Diseases/Infectious diseases/Influenza virus Biological sciences/Immunology/Infection Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Non-pharmaceutical interventions (NPIs) are crucial to control the spread of any Emerging Infectious Disease (EID) 27 when it enters a given population for the first time, particularly when vaccines or effective medications are unavailable. COVID-19, the most recent EID, has provoked another wave of studies on NPIs, including city lockdown 21,23,34,41,43 , test-trace-quarantine 5,11,19,44,48 , shelter-in-place 4 , public mask wearing 15,22,51 , social distancing measures such as school closures and limiting gathering sizes 4,13,22,29,38,41,42,47 , and transportation restriction 41,51 . Since the onset of COVID-19, an extensive body of research has examined the individual or combined effectiveness of these NPIs, e.g. 5,10,16,32 , and has explored optimal strategies to implement NPIs while considering economic or societal factors, e.g. 14,17,18,24-26,31,33,39,46 . Many studies in literature arrive at intuition-consistent conclusions. For example, the greater the stringency of NPIs, the more effective they are at reversing or decelerating the growth rate of the death toll, e.g. 1,23,29,45 , and NPIs should be implemented early and sufficiently long, e.g. 2,6,20,24 . However, contradictory findings have been reported in other studies. For instance, Ref. 7 found that countries with less strict NPIs had lower average confirmed cases and fatality rates; Ref. 22 found no evidence on the effectiveness of test-trace-and-quarantine strategy; and conflicting results have also been reported on the effectiveness of closing schools, workplaces, and businesses, e.g. 22,41,47 . These contradictions underscore that the effectiveness of an NPI fluctuates based on the conditions of their implementation. The effectiveness of an NPI is the result of a function with input parameters that change continuously. These parameters include the stringency of an NPI, the timing to enact an NPI, the virus strain, and the duration of an NPI. A few scholars have coarsely investigated how the timing of initiating or ending an NPI impacts its effectiveness 22,37,41,42,51 . Some suggest that implementing stricter NPIs earlier can enhance their effectiveness, e.g. 23,29 , while others conclude that a higher threshold for triggering or ending NPIs leads to a greater peak in hospitalizations 9 . Nevertheless, these studies did not comprehensively account for the continuous variation of all input parameters. Moreover, these investigations are predominantly focused on scenarios pertaining to the original virus strain 33 and did not assess the effectiveness of NPIs in the context of early or late Omicron variants. Prolonged periods of implementing an NPI may result in significant social well-being costs and economic instability, e.g. 25 . Policymakers confront the difficult decision of selecting NPIs that strike a balance between saving lives and sustaining economic health. Due to limited societal and economic resources, no NPI can endure arbitrarily long, e.g. 31 . Hence, it is beneficial for policymakers to understand which NPI to implement and the optimal time to commence it, especially under the limitations of a predetermined duration. However, this topic has not been studied thoroughly. Most studies assume the duration can be as long as needed. Ref. 30 explored the effects of implementing NPIs for limited periods in idealized settings and discovered that there is an optimal timing to initiate an NPI to ensure its maximum effectiveness. Most previous research has focused on a one-size-fits-all approach to NPIs, applying uniform restrictions across the entire population, e.g. 32 . Few investigations have quantitatively assessed the effectiveness of tailored NPIs for diverse sociodemographic groups 36 . Research on the optimal control strategies for NPIs tends to be theoretical, commonly utilizing simplified Susceptible-Infectious-Recovered (SIR) or Susceptible-Exposed-Infectious-Recovered (SEIR) models, resulting in a lack of practical guidance. Furthermore, these studies usually examine a specific virus strain or analyze the basic reproduction number within a confined range (e.g., ), maintaining other parameters unchanged, and overlook scenarios in which the virus evolves to be more infectious yet less lethal. To bridge the gap in literature and in practice, our paper systematically and comprehensively portrays the dynamics among virus strains, the effectiveness of an NPI, the stringency of an NPI, the timing of initiating an NPI, and the duration of an NPI in effect, capturing not just real-world scenarios of COVID-19 but also exploring theoretical possibilities for all future EIDs, thus encompassing the full range of potential outcomes. Our analysis provides practical and concrete guidance for policymakers in choosing an appropriate NPI and the optimal moment to initiate it by balancing policy effectiveness and associated costs, particularly when its duration must be limited to a specific timeframe. We utilize the extended SEIR model from Ref. 9 , considering the heterogenous infection outcomes across different age groups. This model has undergone meticulous calibration to accurately reflect real-world conditions. Comprehensive data was collected from March 2020 to July 2022, covering all four major COVID-19 variants, to determine model parameter values by age group. These parameters include the transmission rate, contact matrix, hospitalization rate, ICU rate, and mortality rate. For the Delta and Omicron variants, parameter values were estimated using weekly data from the Centers for Disease Control and Prevention (CDC). This comprehensive perspective enables the discovery of the following findings: For any NPI policy in response to a specific COVID-19 variant, there exists an optimal duration beyond which the NPI’s effectiveness plateaus and does not improve with longer periods. If the optimal duration can be attained, implementing the NPI earlier, results in greater effectiveness. If achieving the optimal duration is not feasible, the efficacy of an NPI is contingent upon the timing of its implementation. Starting the policy too late or too early will result in similarly diminished effectiveness. The stricter the policy, the longer the optimal duration tends to be. Therefore, for the most stringent measures, such as city lockdowns or test-trace-quarantine strategies, a nearly indefinite period may be required to maintain low numbers of cases and fatalities. If a stringent policy is implemented for a duration shorter than necessary, its effectiveness will be inferior to that of a less restrictive policy enforced for an equivalent duration. As the virus becomes more contagious (i.e., higher ) and less lethal, the efficacy differential between stringent and less restrictive policies narrows, and the NPI tailored for the vulnerable group can be more effective than a stricter universal policy. Our findings reconcile the contradictions among the previously published studies, as those studies focused on specific segments of a broader global perspective. Our findings also resonate with real-world observations. The stringent test-trace-quarantine strategy implemented in China and at Cornell University successfully maintained minimal case numbers and death tolls from the original strain up to the Omicron variants. When these entities dialed back their policies to mandating face mask wearing, it reflected an acknowledgment that the significantly reduced benefit of maintaining stricter policies could not justify their extensive costs in the context of the Omicron variant. Results NPI policy aims to reduce the rate of contact. For any NPI policy \(\:{P}_{i}\) , such as school closures and stay-at-home order, we assume that the transmission rate \(\:\beta\:\) will be reduced by a certain percentage, \(\:{\pi\:}_{i}\) . Thus, if \(\:{P}_{i}\) is in effect, the effective transmission rate \(\:{\beta\:}_{e}\) will be reduced to \(\:{\beta\:}_{e}=\beta\:(1-{\pi\:}_{i})\) . If multiple policies are in effect at the same time, we assume that the strictest policy will determine the effective transmission rate, i.e., \(\:{\beta\:}_{e}=\beta\:(1-\text{max}{\pi\:}_{i})\) . Specially, this paper considers four NPI policies, as defined in Table 1 . According to Ref. 9 , general social distancing is estimated to reduce contacts by 37.5% across all age groups, while the stay-at-home order is estimated to reduce contacts by 55.1% across all age groups. Social distancing among vulnerable groups is estimated to result in a 50% reduction in contacts among those 60 years and older. A modest social distancing is estimated to result in a 10% contact reduction. The policy of masking has been evidenced to effectively reduce contacts 15 . Ref. 45 found that wearing masks reduces \(\:{R}_{e}\) to \(\:{R}_{0}{\left(1-mp\right)}^{2}\) , where \(\:m\) is the efficacy of trapping viral particles inside the mask, and \(\:p\) is the percentage of the population that wears masks. With 50% mask usage and 50% mask efficacy level, \(\:{R}_{e}\) will be reduced to 0.56 \(\:{R}_{0}\) . It is equivalent to reducing contacts across all age group by 34%. The effect of 50% mask usage and 50% mask efficacy level is approximately equal to Policy 1: a general social distancing. The timing of initiating or ending an NPI significantly affects number of hospitalizations, ICU admissions, and deaths. If a policy is lifted prematurely, the infected cases can bounce back rapidly, potentially spiraling the situation out of control. Conversely, maintaining a policy longer than necessary can lead to elevated economic and social costs. Estimating the economic and social cost of a certain policy is complex and beyond the scope of our paper. For simplicity, we use the duration that an NPI policy is in effect as a proxy of the policy cost. We assume that the policy cost is an increasing function of the policy duration. Longer duration would result in higher economic and social costs. Note that the relationship between policy cost and policy duration can be non-linear. Table 1 Non-pharmaceutical Intervention Policies Policy Definition and Example Estimated Contact Reduction 1 General social distancing (e.g., the policies in effect from March 23 – March 27, 2020, in Minnesota, including K-12 school closures and work-from-home recommendations; or mandatory masking) 37.5% 2 Shelter-in-place policy (e.g., the Minnesota’s stay-at-home order that began March 28, 2020) 55.1% 3 Social distancing for vulnerable groups (i.e., 60 + years old) 50% among the vulnerable groups, 0% among others 4 Modest social distancing that may be sustained once other measures are ended. 10% The Timing to End an NPI policy. We use the peak ICU occupancy to illustrate the policy effectiveness. Figure 1a plots the peak number of ICU patients in a day during the pandemics under the original COVID-19 virus, as the duration of Policy 1 (general social distancing) increases. Each line in Fig. 1a corresponds to the day that Policy 1 is initiated. For simplicity, Fig. 1 only plots a sample of initiation days. As the duration of Policy 1 increases, the peak number of ICU patients in a day decreases but stops decreasing at a certain duration. After this point, increasing the duration of a policy will not further reduce the peak number of hospitalized patients. From the perspective of not overwhelming the healthcare system, the corresponding policy duration can be considered the optimal one, and policymaker should end the policy after this point. The optimal policy duration varies if the policy starting day differs. As shown in Fig. 1, the later a policy starts, the shorter the optimal policy duration will be. It is because if an NPI policy were enacted late into the pandemic, the virus would have already spread among the population. Policies 2 to 4 also present similar patterns in other metrics (e.g., peak infections, peak hospitalizations, and total deaths) across all four virus variants. It is important to note that, in contrast to other metrics, enacting an NPI policy consistently lowers the total number of deaths as long as the policy remains active. However, there exists an optimal threshold beyond which the reduction in total deaths slows down significantly, approaching a near-zero rate of decrease. Across all virus strains, Policy 2 consistently proves to be the most effective, while Policy 4 remains the least effective. This outcome aligns with the level of strictness associated with each policy; Policy 2, which mandates shelter in place, is the most stringent, whereas Policy 4, modest social distancing, is the least strict. As a virus variant increases in transmissibility (for instance, evolving from the original strain to late Omicron), the effectiveness of an NPI policy decreases (see Fig. 1), but the optimal duration needed for the policy is reduced. For example, if Policy 1 is implemented 13 days (roughly two weeks) post-outbreak, the policy must last over 66 days to minimize the peak ICU occupancy against the original virus (see Fig. 1a), but only 25 days are needed against late Omicron (see Fig. 1b). Moreover, as the virus becomes more transmissible, the window of opportunity for policymakers to act effectively narrows. For instance, implementing Policy 1, 43 days after the original virus outbreak can still effectively reduce the peak ICU occupancy. Yet, it would not be effective at all if applied 43 days following the outbreak of late Omicron (see Fig. 1). Policy 1 (general social distancing/masking) is not as effective at reducing peak ICU occupancy as Policy 3 (targeted social distancing for vulnerable groups) when the predominant strain is early or late Omicron. Figure 2 demonstrates that Policy 3 can reduce peak ICU occupancy to a lower level than Policy 1 if the policy is in effect sufficiently long. This is a reversal from the situation with the original virus and Delta variant. Both the early and late Omicron variants are more contagious but less deadly than the preceding strains. Policy 3, considered less stringent, incurs lower economic and social costs than Policy 1 because it focuses on vulnerable groups rather than the entire population. Consequently, Policy 3 emerges as a preferable strategy when the dominant virus is highly transmissible (e.g., \(\:{R}_{0}>5\) ) but poses less risk to those who are not vulnerable. It is noteworthy that enacting a policy immediately after the emergence of a highly transmissible virus (e.g., \(\:{R}_{0}>10\) ) requires that the policy remains in place sufficiently long. Failing to do so could lead to a greater strain on the healthcare system (e.g., higher peak ICU occupancy and hospitalizations) than taking no action at all. This effect is especially marked with Policy 3 during the early and late Omicron outbreaks. For instance, as seen in Fig. 4, with the late Omicron variant, if Policy 3 is implemented just one-week post-outbreak, the peak ICU occupancy could surpass that of a no-policy scenario unless Policy 3 remains active for more than 14 days. This particular outcome does not extend to the metric of total deaths, indicating that while prematurely ending an NPI policy might increase healthcare system strain, it does not necessarily affect the total death count. The Timing to Initiate an NPI policy In practice, it is not feasible for a government to implement policies that restrict daily life for an extended period. The stricter the policy, the shorter the duration it can be sustained by the government. For instance, a Governor of a State in the United States can declare a state of emergency with the authority to enact certain measures, but only for a limited term. Therefore, we aim to investigate the optimal timing for implementing a policy, considering the constrained duration for which the policy can remain in effect. Figure 3 displays the peak ICU occupancy for the original virus strain under various policies, considering different durations of policy implementation. With the original virus strain, the stricter the policy, the lower the peak in ICU occupancy. For instance, a shelter-in-place policy (Policy 2) would most significantly reduce peak ICU occupancy compared to the other three policies. If it is feasible for a policy to remain in effect for an extended period, initiating the policy earlier is advantageous, as it tends to result in lower peak ICU occupancy. However, the trade-off is that a longer duration of policy implementation incurs higher economic and social costs. Figure 3 reveals that initiating a policy as early as possible is not the most effective strategy, unless the policy is maintained for a prolonged period (e.g., 84 days for Policy 1). There exists an optimal initiating time between Day 1 and Day 53 (the day ICU occupancy is projected to reach its peak without intervention). A shorter policy duration would shift the optimal initiating time to a later point. For example, as shown in Fig. 2 , if a policymaker can only enforce Policy 1 for two weeks (14 days), the optimal initiating time would be Day 43. Initiating Policy 1 any earlier than Day 43, with it lasting only 14 days, would lead to a higher peak in ICU occupancy. A similar pattern is evident with other virus variants and metrics (e.g., peak infections, peak hospitalizations, and total deaths). When the prevailing virus strain is more transmissible, the optimal timing to initiate a policy for a specific duration moves to an earlier date. For example, as depicted in Fig. 4a, with the late Omicron variant, if a policymaker is limited to enforcing Policy 1 for only two weeks, the optimal initiating time would be Day 19, compared to Day 43 for the original virus strain (see Fig. 3 ). Total deaths can serve as an indicator that prioritizes life-saving measures above economic and social costs. When examining Fig. 4a against Fig. 4b, it is evident that the best time to implement a policy varies between minimizing peak ICU occupancy and total deaths. For instance, in the scenario involving the late Omicron variant and a two-week enforcement of Policy 1, the optimal initiating day to minimize total deaths is Day 25, whereas it is Day 19 to minimize peak ICU occupancy. Initiating Policy 1 on Day 25 instead of Day 19 to minimize the total deaths necessitates an approximate 8% increase in the ICU capacity. This suggests that healthcare systems may need to endure a greater load to prevent more virus-related deaths. Such phenomenon is observed across all four policies and any given duration that the optimal initiating day of a policy to achieve the minimal total deaths consistently occurs later than that for minimizing peak ICU occupancy. Policymakers typically require some time to respond after the outbreak of a pandemic and are unable to maintain intervention policies indefinitely. Our findings offer encouraging insights for policymakers, suggesting that, to avoid overwhelming the healthcare system, there is no immediate need for action assuming the virus cannot be eradicated. Instead, it is optimal to delay the implementation of NPIs for a certain period. Nevertheless, if the dominant virus strain is highly transmissible, decision-makers must act more swiftly. Discussion Results of our study extend the understanding of policy effectiveness in the literature. For example, Ref. 15 studied the original virus and concluded that wearing mask should be widespread, rather than limited to susceptible or infectious individuals. Ref. 29 reviewed data from 32 countries with varying levels of policy strictness under the original virus and found that the higher the strength of government interventions at early stages, the more effective the policy was at reversing or slowing growth of death rate. Our results demonstrate that these are only true for the original virus but not for the more transmissible variants (e.g., \(\:{R}_{0}>5\) ). The widespread masking policy is less effective, e.g., peak ICU, peak hospitalizations, and deaths than social distancing for the vulnerable group against Omicron. In Minnesota, the Governor started the Stay Home Order on 3/28/2020 when 441 cumulative confirmed cases and 5 cumulative deaths were recorded, and the order remained in effect until 5/18/2020, for a total of 54 days. Since the order was enacted on Day 7, i.e., 3/28/2020, our model’s results indicate that the best timing to end it should have been on Day 111 with a duration of 104 days, in terms of lowest possible peak ICU occupancy, or later than Day 150 in terms of the total deaths. The longest duration used in the numerical experiment is 150 days. The total deaths have not reached its lowest level on Day 150 if the Stay Home Order is enacted on Day 7. If the Governor was only able to keep the order in effect for 54 days, then the best timing to enact the Stay Home Order in Minnesota would have been on Day 28 to achieve the lowest peak ICU occupancy, or on Day 40 to minimize total deaths. Interestingly, our model shows that if a policy is enacted on Day 7, kept for 54 days, with no other policies, the Stay Home Order (Policy 2) results in the highest total deaths (45.6K) by Day 365, compared to Policy 1 (44.5K), Policy 3 (37.7K), and Policy 4 (45.3K). Policy 2 also leads to the second highest peak ICU occupancy (5.0K), while Policy 1 results in 4.6K, Policy 3 in 4.5K, and Policy 4 in 5.1K. The best policy under these conditions is Policy 3 (social distancing for vulnerable groups), as it achieves the lowest peak ICU and total deaths, with lower social and economic costs. This suggests that stricter policies need to be in effect longer to be effective. If not, outcomes could be worse than with less strict policies, making the additional costs unjustified. The necessary duration of a policy shortens with increased virus transmissibility. The test-trace-quarantine policy is a suppression policy, which requires “high testing and tracing rates, high quarantine compliance, relatively short testing and tracing delays, and moderate to high mask use” 19 . This policy aims to minimize the total infections rather than prevent the healthcare system from being overwhelmed. When effectively implemented, this approach can significantly reduce the transmission rate, potentially bringing it nearly to zero. According to Figure A1 in the Appendix III, if the strictest policy, with a 99% reduction of the contact rate (e.g., test-trace-quarantine policy), were enacted on Day 1 and lasted for 150 days, the peak ICU occupancy and the total number of deaths would almost be equivalent to the situation where no policies were used. This result suggests that such a strict policy cannot be lifted if the highly transmissible virus is not eradicated. Otherwise, the policy only delays the outbreak of the pandemic without reducing the total number of infections or deaths. Once lifted, the pandemic will begin anew. Thus, the test-trace-quarantine policy should be employed to buy time for the development of vaccines and effective treatments, or until the virus is eradicated. Cornell University is one example that successfully implemented this policy for as long as they could. Cornell University reopened for in-person instruction in Fall 2020, when the original virus was dominant, one of the earliest universities in the US to reopen during the pandemic. It implemented an asymptomatic screening program based on an SEIR model to test students regularly and test varsity athletes and students in Greek-life organizations even more frequently 11 . Due to the specific settings of Cornell University, a near-closed community with a relatively small-scale total population, of which the majority is young and healthy; the compliance of this policy was high. Combining with mandatory vaccination, it succeeded in controlling campus outbreaks until Omicron hit in December 2021, which forced the university to shut down its campus 35 . Cornell maintained their COVID restrictions as the New York State dropped its mask mandates in March 2022 12 . However, there was no severe illness in any of the infected students at Cornell since fall 2020 12 . From a 20/20 hindsight perspective, the number of infections might not be the best objective to determine NPI policies. Applying our results to the settings of Cornell University, the test-trace-quarantine policy might not be the most cost-effective strategy. We would recommend that Cornell University require social distancing for the vulnerable group only, particularly after the vaccine became available or when the virus was highly transmissible, e.g., Omicron, while imposing no restrictions for others. China is another example that implemented such a policy on a large scale, “dynamic Zero-COVID” policy, from January 2020 to January 8, 2023 44 . Due to the high compliance to the policy enforced by the government, it succeeded in keeping the number of COVID deaths low, about 6,000 deaths recorded among 1.4 billion people in China 8 . According to our results, the suppression policy cannot be lifted until the virus is eradicated. China implemented the strictest policy early in the pandemic and maintained it for approximately three years, which allowed them to outlast the original and Delta variants. This approach ensured that the policy remained in effect long enough to achieve its intended goals. The country has, however, paid incredibly high social and economic costs, such as extremely harsh and severe restrictions on people's movements. This policy was no longer sustainable when Omicron hit. As the virus becomes more transmissible and less deadly, a better objective to manage the pandemic would be not to overwhelm the healthcare system rather than minimizing the infections. For example, if a policy is enacted on Day 7 under the late Omicron, our results show that Policy 3 needs to stay in place for 25 days to reach the lowest peak ICU occupancy of 4.2K a day and Policy 2 needs to stay in place for 30 days to reach the lowest peak ICU of 3.9K a day. Policy 3 is a good balance between the social costs and the burden on the healthcare system. Although the specific number cannot be directly translated into situations in China, the general conclusion applies to China, that Policy 3, social distancing for vulnerable groups, should be the best policy to use when Omicron was the dominant variant, rather than the strictest dynamic Zero-COVID policy. The optimal timing for initiating or terminating a policy is contingent upon the virus's transmissibility. There exists an ideal duration for a policy, beyond which no additional reduction in the peak burden on the healthcare system can be achieved. Note that extending an NPI beyond its ideal duration will continue to reduce overall infections and deaths. Lifting the policy after this period could cause ICU occupancy to rebound, but it would not exceed its previous peak level. With higher transmissibility of the virus, a shorter duration of the policy is required, necessitating a more rapid response time for decision-makers to implement an NPI policy. Should a stringent policy be implemented for a duration that is insufficient, its efficacy may be less than that of a less restrictive policy applied over the same period, potentially yielding outcomes worse than taking no action at all against a highly transmissible virus, e.g., Omicron. For a fixed duration of a policy, it is not always optimal to initiate the policy at the onset of the pandemic. The shorter the policy duration, the later it should be introduced into the pandemic timeline. Essentially, if a strict NPI policy like lockdowns cannot be sustained long enough, policymakers should not implement such stringent measures at the onset of a pandemic. Instead, policymakers should consider enacting these policies later in the pandemic for maximum effectiveness. This applies when virus eradication is infeasible, as with COVID-19 28 . If eradication is possible, most effective policy is a suppression strategy, such as test-trace-quarantine, as seen in the 2003 SARS outbreak 50 . If suppression policy cannot be maintained until eradication or vaccines are available, we recommend switching to mitigation policies. Given that hospitalization, ICU admission, and mortality rates vary among different groups, optimal NPI policy should balance social costs and total deaths, targeting strategies based on the virus's transmissibility. For highly transmissible but less lethal variants (e.g., Omicron), social distancing for vulnerable groups is best. For less transmissible variants (e.g., the original virus, Delta, \(\:{R}_{0}<5\) ), widespread masking is more effective. Modest social distancing is nearly ineffective against highly transmissible viruses. Methods To examine the balance between policy effectiveness and policy cost, we consider the following factors, including the virus variant, NPI policy, policy starting day, and policy duration (see Table 2 ). NPI policy refers to the four policies in Table 2 , each of which has different effectiveness in terms of the reduction to the transmission rate of a virus variant. The four NPI policies can be ordered by its strictness as Policy 2 > Policy 1 > Policy 3 > Policy 4, where Policy 2 is the strictest. Policy starting day refers to the day that a policy is enacted, and Policy duration refers to how many days a policy is in effect. Table 2 Factor and Level. We run the model with initial parameter settings (as in Table A1) without any intervention policies and the number of patients in ICU peaks at Day 53. Thus, we set 53 as the last meaningful day to start a policy. Factor Levels COVID-19 variant original virus, delta, early omicron, late omicron NPI Policy 1, 2, 3, 4 Policy starting day 1, 4, 7, …, 53 Policy duration 1, 2, 3, …, 150 The COVID-19 virus variant includes the original virus (SARS-CoV-2), delta, early omicron, and late omicron. The original virus was first identified in China in December 2019 and arrived in the U.S. in early January 2020; the Delta variant was first detected in India in October 2020 and detected in the U.S. in February 2021; the early Omicron variant, e.g., BA.1, BA.2 was first detected in South Africa in November 2021 and in the U.S. in December 2021; the late omicron, e.g., BA.4 and BA.5 became dominant in the U.S. in June 2022 49 . Table 3 displays the estimated values of the major parameters of these variants that are used in this experimental study. According to the transmissibility, i.e., \(\:{R}_{0}\) of a virus variant, the four variants considered in the experiment are ordered as Late Omicron > Early Omicron > Delta > the original. Table 3 Estimated Values of Major Parameter by COVID-19 Variants . The parameters for the original virus are calibrated using the COVID19 cases in Minnesota from March 23 through April 25, 2020, by Ref 9 . The parameters of the other variants are obtained mainly from the CDC reports. The rate of hospitalized, the rate of ICU, and the rate of death are the average rates across all age group. We refer readers to the Appendix II for further details and data sources. COVID-19 variant \(\:{\varvec{R}}_{0}\) Rate of Hospitalized Rate of ICU Rate of Death Original 3.87 0.0353 0.2301 0.0153 Delta 5.08 0.0796 0.1765 0.0123 Early Omicron 9.5 0.0683 0.1331 0.0053 Late Omicron 13.3 0.0377 0.1330 0.0028 The SEIR model and its extensions have been widely used to study infectious diseases, e.g. 3 . We adopt the SEIR-type model used by the Minnesota government 9 to replicate the COVID-19 pandemic. The model (see Fig. 5 ) extended the typical SEIR model by including multiple exposed states E, multiple asymptomatic (AI) and symptomatic (I) infectious states, a component H to capture the information of hospitalizations (non-ICU), a component ICU to capture the information of patients who are currently in ICUs, and a component D to capture the information of deaths. This model also includes population stratification and age-specific mixing patterns. We include the specific parameter settings in Appendix I and refer readers to 9 for more details of the model. To make a fair comparison, we use the same initial settings for all variants. On Day 0, there were 201 infectious cases, 26 were hospitalized, 6 were in the ICU, and no deaths. The total population is set to be 5.69 million. Note that the parameters of all the virus variants are empirically estimated based on the reported hospital data. Thus, the parameters, such as death rate, and hospitalized rate of later variants, e.g., delta and omicron are already considered the background immunity level, either from the earlier infection or the vaccinations in the population. COVID-19 virus is unlikely to be eradicated and we are more likely to live with it 28 . Thus, rather than focusing on the total number of infections, hospitalizations, and deaths, our study focuses on the burden on healthcare resources, e.g., ICU beds due to COVID-19 virus. Infectious diseases should be managed to ensure that healthcare capacity is not exceeded, allowing individuals to receive the quality of care necessary to avoid unnecessary suffering or deaths. Thus, this paper uses the following criteria to evaluate the effectiveness of a given policy, the number of patients being hospitalized at a given day, and the number of COVID-19 patients being in ICU at a given day, and the total deaths, where the first two reflects the burden on the healthcare system and the last one reflects the ultimate severity and impact of the disease on the population. Declarations Author contributions statement C.X., S.K. and Y.M. conceptualized and designed the study, worked on curation of data, and contributed to the interpretation of results. C.X., and Y.M. drafted the manuscript. N.G., and C.C. worked on curation of data, worked on interpretation of results, and revision of the manuscript. All authors have read and approved the final manuscript. Funding There was no funding for this research. Competing interests The authors declare no competing interests. Data availability All data generated or analysed during this study are included in this published article [and its supplementary information files] Additional information Supplementary information is provided in Appendix I and Appendix II. Correspondence and requests for materials should be addressed to C.C. References Ayouni, I. et al. Effective public health measures to mitigate the spread of COVID-19: a systematic review. BMC Public Health . 21, 1015 (2021). Balderrama, R. et al. Optimal control for a SIR epidemic model with limited quarantine. Sci Rep . 12, 12583 (2022). https://doi.org/10.1038/s41598-022-16619-z Bjørnstad, O. N. et al. The SEIRS model for infectious disease dynamics. Nat Methods. 17, 557–558 (2020). https://doi.org/10.1038/s41592-020-0856-2 Brauner J. M. et al. Inferring the effectiveness of government interventions against COVID-19. Science . 371, (6531) (2020). 10.1126/science.abd9338 Chan, T. C. et al. 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Prater, N. and Walsh, J. D. How Omicron Pushed Cornell Into Red Alert A huge COVID outbreak has shut down the Ivy League campus and could be a sign of what’s to come. Intelligencer . Preprint at https://nymag.com/intelligencer/2021/12/how-omicron-pushed-cornell-into-red-alert.html (2021). Richard Q, et al. Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic. PLOS Computational Biology . 17(3) , (2021). e1008776. https://doi.org/10.1371/journal.pcbi.1008776 Sanstead EC, Li Z, McKearnan SB, et al. Adaptive COVID-19 Mitigation Strategies: Tradeoffs between Trigger Thresholds, Response Timing, and Effectiveness. MDM Policy & Practice . 8(2) (2023). doi:10.1177/23814683231202716 Sharma, M. et al. Understanding the effectiveness of government interventions against the resurgence of COVID-19 in Europe. Nat Commun . 12 , 5820, (2021). https://doi.org/10.1038/s41467-021-26013-4 Silva, C. J. et al. Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal. Sci Rep . 11, 3451 (2021). https://doi.org/10.1038/s41598-021-83075-6 Strong, A. & Welburn, J. W. An Estimation of the Economic Costs of Social-Distancing Policies. Santa Monica, CA: RAND Corporation. Preprint at https://www.rand.org/pubs/research_reports/RRA173-1.html (2020). Sun, K. S. et al. Effectiveness of different types and levels of social distancing measures: a scoping review of global evidence from earlier stage of COVID-19 pandemic. BMJ Open . (2022). doi: 10.1136/bmjopen-2021-053938 Suwantika, A. A. et al. The cost-effectiveness of social distancing measures for mitigating the COVID-19 pandemic in a highly-populated country: A case study in Indonesia. Travel Medicine and Infectious Disease . 45, (2022). ISSN 1477-8939. https://doi.org/10.1016/j.tmaid.2021.102245. Tellis, G. J., et al. Lockdown Without Loss? A Natural Experiment of Net Payoffs from COVID-19 Lockdowns. Journal of Public Policy & Marketing . 42(4), (2023). The Lancet Regional Health – Western Pacific. The end of zero-COVID-19 policy is not the end of COVID-19 for China, Editorial, The Lancet . Preprint at https://www.thelancet.com/journals/lanwpc/article/PIIS2666-6065(23)00020-2/fulltext (2023). Tian, L. et al. Calibrated intervention and containment of the COVID-19 pandemic. Nature Communications . 12, 1147 (2021). Tsay, C. et al. Modeling, state estimation, and optimal control for the US COVID-19 outbreak. Sci Rep . 10, 10711 (2020). https://doi.org/10.1038/s41598-020-67459-8 Viner R. M. et al. School closure and management practices during coronavirus outbreaks including COVID-19: a rapid systematic review. Lancet Child Adolesc Health , 4, 397–404 (2020). pmid:32272089 Wells, C. R. et al. Optimal COVID-19 quarantine and testing strategies. Nat Commun . 12, 356 (2021). https://doi.org/10.1038/s41467-020-20742-8 Wikipedia, Variants of SARS-CoV-2, https://en.wikipedia.org/wiki/Variants_of_SARS-CoV-2 Wilder-Smith, A. et al. Can we contain the COVID-19 outbreak with the same measures as for SARS? Lancet Infect Dis , 20(5) , e102–07 (2020). Zhou L. et al. Cost-effectiveness of interventions for the prevention and control of COVID-19: Systematic review of 85 modelling studies. J Glob Health . (2022). doi: 10.7189/jogh.12.05022. PMID: 35712857; PMCID: PMC9196831. Additional Declarations No competing interests reported. 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COVID-19, the most recent EID, has provoked another wave of studies on NPIs, including city lockdown\u003csup\u003e21,23,34,41,43\u003c/sup\u003e, test-trace-quarantine\u003csup\u003e5,11,19,44,48\u003c/sup\u003e, shelter-in-place\u003csup\u003e4\u003c/sup\u003e, public mask wearing\u003csup\u003e15,22,51\u003c/sup\u003e, social distancing measures such as school closures and limiting gathering sizes\u003csup\u003e4,13,22,29,38,41,42,47\u003c/sup\u003e, and transportation restriction\u003csup\u003e41,51\u003c/sup\u003e. Since the onset of COVID-19, an extensive body of research has examined the individual or combined effectiveness of these NPIs, e.g.\u003csup\u003e5,10,16,32\u003c/sup\u003e, and has explored optimal strategies to implement NPIs while considering economic or societal factors, e.g.\u003csup\u003e14,17,18,24-26,31,33,39,46\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMany studies in literature arrive at\u0026nbsp;intuition-consistent conclusions. For example, the greater the stringency of NPIs, the more effective they are at reversing or decelerating the growth rate of the death toll, e.g.\u003csup\u003e1,23,29,45\u003c/sup\u003e, and NPIs should be implemented early and sufficiently long, e.g.\u003csup\u003e2,6,20,24\u003c/sup\u003e. However, contradictory findings have been reported in other studies. For instance, Ref.\u003csup\u003e7\u003c/sup\u003e found that countries with less strict NPIs had lower average confirmed cases and fatality rates; Ref.\u003csup\u003e22\u003c/sup\u003e found no evidence on the effectiveness of test-trace-and-quarantine strategy; and conflicting results have also been reported on the effectiveness of closing schools, workplaces, and businesses, e.g.\u003csup\u003e22,41,47\u003c/sup\u003e. These contradictions underscore that the effectiveness of an NPI fluctuates based on the conditions of their implementation.\u003c/p\u003e\n\u003cp\u003eThe effectiveness of an\u0026nbsp;NPI is\u0026nbsp;the\u0026nbsp;result of a function with input parameters that change continuously. These parameters include the stringency of an NPI, the timing to enact an NPI, the virus strain, and the duration of an NPI. A few scholars have coarsely investigated how the timing of initiating or ending an NPI impacts its effectiveness\u003csup\u003e22,37,41,42,51\u003c/sup\u003e. Some suggest that implementing stricter NPIs earlier can enhance their effectiveness, e.g.\u003csup\u003e23,29\u003c/sup\u003e, while others conclude that a higher threshold for triggering or ending NPIs leads to a greater peak in hospitalizations\u003csup\u003e9\u003c/sup\u003e. Nevertheless, these studies did not comprehensively account for the continuous variation of all input parameters. Moreover, these investigations are predominantly focused on scenarios pertaining to the original virus strain\u003csup\u003e33\u003c/sup\u003e and did not assess the effectiveness of NPIs in the context of early or late Omicron variants.\u003c/p\u003e\n\u003cp\u003eProlonged periods of implementing an NPI may result in significant social well-being costs and economic instability, e.g.\u003csup\u003e25\u003c/sup\u003e. Policymakers confront the difficult decision of selecting NPIs that strike a balance between saving lives and sustaining economic health.\u0026nbsp;Due to limited societal and economic resources, no NPI can endure arbitrarily long, e.g.\u003csup\u003e31\u003c/sup\u003e. Hence, it is beneficial for policymakers to understand which NPI to implement and the optimal time to commence it, especially under the limitations of a predetermined duration. However, this topic has not been studied thoroughly.\u0026nbsp;Most studies assume the duration can be as long as needed. Ref.\u003csup\u003e30\u003c/sup\u003e explored the effects of implementing NPIs for limited periods in idealized settings and discovered that there is an optimal timing to initiate an NPI to ensure its maximum effectiveness.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMost previous research has focused on a one-size-fits-all approach to NPIs, applying uniform restrictions across the entire population, e.g.\u003csup\u003e32\u003c/sup\u003e. Few investigations have quantitatively assessed the effectiveness of tailored NPIs for diverse sociodemographic groups\u003csup\u003e36\u003c/sup\u003e. Research on the optimal control strategies for NPIs tends to be theoretical, commonly utilizing simplified Susceptible-Infectious-Recovered (SIR) or Susceptible-Exposed-Infectious-Recovered (SEIR) models, resulting in a lack of practical guidance. Furthermore, these studies usually examine a specific virus strain or analyze the basic reproduction number within a confined range (e.g.,\u0026nbsp;\u0026nbsp;), maintaining other parameters unchanged, and overlook scenarios in which the virus evolves to be more infectious yet less lethal.\u003c/p\u003e\n\u003cp\u003eTo bridge the gap in literature and in practice, our paper systematically and comprehensively portrays the dynamics among virus strains, the effectiveness of an NPI, the stringency of an NPI, the timing of initiating an NPI, and the duration of an NPI in effect, capturing not just real-world scenarios\u0026nbsp;of COVID-19\u0026nbsp;but also exploring theoretical possibilities\u0026nbsp;for all future EIDs, thus encompassing the full range of potential outcomes. Our analysis provides practical and concrete guidance for policymakers in choosing an appropriate NPI and the optimal moment to initiate it by balancing policy effectiveness and associated costs, particularly when its duration must be limited to a specific timeframe.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe utilize the extended SEIR model from Ref.\u003csup\u003e9\u003c/sup\u003e, considering the heterogenous infection outcomes across different age groups. This model has undergone meticulous calibration to accurately reflect real-world conditions. Comprehensive data was collected from March 2020 to July 2022, covering all four major COVID-19 variants, to determine model parameter values by age group. These parameters include the transmission rate, contact matrix, hospitalization rate, ICU rate, and mortality rate. For the Delta and Omicron variants, parameter values were estimated using weekly data from the Centers for Disease Control and Prevention (CDC). This comprehensive perspective enables the discovery of the following findings:\u003c/p\u003e\n\u003col\u003e\n \u003cli\u003eFor any NPI policy in response to a specific COVID-19 variant, there exists an optimal duration beyond which the NPI’s effectiveness plateaus and does not improve with longer periods.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eIf the optimal duration can be attained, implementing the NPI earlier, results in greater effectiveness.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eIf achieving the optimal duration is not feasible, the efficacy of an NPI is contingent upon the timing of its implementation. Starting the policy too late or too early will result in similarly diminished effectiveness.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eThe stricter the policy, the longer the optimal duration tends to be. Therefore, for the most stringent measures, such as city lockdowns or test-trace-quarantine strategies, a nearly indefinite period may be required to maintain low numbers of cases and fatalities.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eIf a stringent policy is implemented for a duration shorter than necessary, its effectiveness will be inferior to that of a less restrictive policy enforced for an equivalent duration.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eAs the virus becomes more contagious (i.e., higher\u0026nbsp;\u0026nbsp;) and less lethal, the efficacy differential between stringent and less restrictive policies narrows, and the NPI tailored for\u0026nbsp;the vulnerable group can be more effective than a stricter universal policy.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eOur findings reconcile the contradictions among the previously published studies, as those studies focused on specific segments of a broader global perspective. Our findings also resonate with real-world observations. The stringent test-trace-quarantine strategy implemented in China and at Cornell University successfully maintained minimal case numbers and death tolls from the original strain up to the Omicron variants. When these entities dialed back their policies to mandating face mask wearing, it reflected an acknowledgment that the significantly reduced benefit of maintaining stricter policies could not justify their extensive costs in the context of the Omicron variant.\u0026nbsp;\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eNPI policy aims to reduce the rate of contact. For any NPI policy \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{i}\\)\u003c/span\u003e\u003c/span\u003e, such as school closures and stay-at-home order, we assume that the transmission rate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\beta\\:\\)\u003c/span\u003e\u003c/span\u003e will be reduced by a certain percentage, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\pi\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e. Thus, if \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{i}\\)\u003c/span\u003e\u003c/span\u003e is in effect, the effective transmission rate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{e}\\)\u003c/span\u003e\u003c/span\u003e will be reduced to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{e}=\\beta\\:(1-{\\pi\\:}_{i})\\)\u003c/span\u003e\u003c/span\u003e. If multiple policies are in effect at the same time, we assume that the strictest policy will determine the effective transmission rate, i.e., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{e}=\\beta\\:(1-\\text{max}{\\pi\\:}_{i})\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eSpecially, this paper considers four NPI policies, as defined in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. According to Ref.\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e, general social distancing is estimated to reduce contacts by 37.5% across all age groups, while the stay-at-home order is estimated to reduce contacts by 55.1% across all age groups. Social distancing among vulnerable groups is estimated to result in a 50% reduction in contacts among those 60 years and older. A modest social distancing is estimated to result in a 10% contact reduction. The policy of masking has been evidenced to effectively reduce contacts\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Ref.\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e found that wearing masks reduces \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{e}\\)\u003c/span\u003e\u003c/span\u003e to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{0}{\\left(1-mp\\right)}^{2}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m\\)\u003c/span\u003e\u003c/span\u003e is the efficacy of trapping viral particles inside the mask, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\)\u003c/span\u003e\u003c/span\u003e is the percentage of the population that wears masks. With 50% mask usage and 50% mask efficacy level, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{e}\\)\u003c/span\u003e\u003c/span\u003e will be reduced to 0.56\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{0}\\)\u003c/span\u003e\u003c/span\u003e. It is equivalent to reducing contacts across all age group by 34%. The effect of 50% mask usage and 50% mask efficacy level is approximately equal to Policy 1: a general social distancing.\u003c/p\u003e\n\u003cp\u003eThe timing of initiating or ending an NPI significantly affects number of hospitalizations, ICU admissions, and deaths. If a policy is lifted prematurely, the infected cases can bounce back rapidly, potentially spiraling the situation out of control. Conversely, maintaining a policy longer than necessary can lead to elevated economic and social costs. Estimating the economic and social cost of a certain policy is complex and beyond the scope of our paper. For simplicity, we use the duration that an NPI policy is in effect as a proxy of the policy cost. We assume that the policy cost is an increasing function of the policy duration. Longer duration would result in higher economic and social costs. Note that the relationship between policy cost and policy duration can be non-linear.\u0026nbsp;\u003c/p\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eNon-pharmaceutical Intervention Policies\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePolicy\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDefinition and Example\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEstimated Contact Reduction\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGeneral social distancing (e.g., the policies in effect from March 23 \u0026ndash; March 27, 2020, in Minnesota, including K-12 school closures and work-from-home recommendations; or mandatory masking)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e37.5%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eShelter-in-place policy (e.g., the Minnesota\u0026rsquo;s stay-at-home order that began March 28, 2020)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e55.1%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSocial distancing for vulnerable groups (i.e., 60\u0026thinsp;+\u0026thinsp;years old)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e50% among the vulnerable groups,\u003c/p\u003e\n \u003cp\u003e0% among others\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eModest social distancing that may be sustained once other measures are ended.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe Timing to End an NPI policy.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe use the peak ICU occupancy to illustrate the policy effectiveness. Figure\u0026nbsp;1a plots the peak number of ICU patients in a day during the pandemics under the original COVID-19 virus, as the duration of Policy 1 (general social distancing) increases. Each line in Fig.\u0026nbsp;1a corresponds to the day that Policy 1 is initiated. For simplicity, Fig.\u0026nbsp;1 only plots a sample of initiation days. As the duration of Policy 1 increases, the peak number of ICU patients in a day decreases but stops decreasing at a certain duration. After this point, increasing the duration of a policy will not further reduce the peak number of hospitalized patients. From the perspective of not overwhelming the healthcare system, the corresponding policy duration can be considered the optimal one, and policymaker should end the policy after this point.\u003c/p\u003e\n\u003cp\u003eThe optimal policy duration varies if the policy starting day differs. As shown in Fig.\u0026nbsp;1, the later a policy starts, the shorter the optimal policy duration will be. It is because if an NPI policy were enacted late into the pandemic, the virus would have already spread among the population. Policies 2 to 4 also present similar patterns in other metrics (e.g., peak infections, peak hospitalizations, and total deaths) across all four virus variants. It is important to note that, in contrast to other metrics, enacting an NPI policy consistently lowers the total number of deaths as long as the policy remains active. However, there exists an optimal threshold beyond which the reduction in total deaths slows down significantly, approaching a near-zero rate of decrease. Across all virus strains, Policy 2 consistently proves to be the most effective, while Policy 4 remains the least effective. This outcome aligns with the level of strictness associated with each policy; Policy 2, which mandates shelter in place, is the most stringent, whereas Policy 4, modest social distancing, is the least strict.\u003c/p\u003e\n\u003cp\u003eAs a virus variant increases in transmissibility (for instance, evolving from the original strain to late Omicron), the effectiveness of an NPI policy decreases (see Fig. 1), but the optimal duration needed for the policy is reduced. For example, if Policy 1 is implemented 13 days (roughly two weeks) post-outbreak, the policy must last over 66 days to minimize the peak ICU occupancy against the original virus (see Fig. 1a), but only 25 days are needed against late Omicron (see Fig. 1b). Moreover, as the virus becomes more transmissible, the window of opportunity for policymakers to act effectively narrows. For instance, implementing Policy 1, 43 days after the original virus outbreak can still effectively reduce the peak ICU occupancy. Yet, it would not be effective at all if applied 43 days following the outbreak of late Omicron (see Fig. 1).\u003c/p\u003e\n\u003cp\u003ePolicy 1 (general social distancing/masking) is not as effective at reducing peak ICU occupancy as Policy 3 (targeted social distancing for vulnerable groups) when the predominant strain is early or late Omicron. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e demonstrates that Policy 3 can reduce peak ICU occupancy to a lower level than Policy 1 if the policy is in effect sufficiently long. This is a reversal from the situation with the original virus and Delta variant. Both the early and late Omicron variants are more contagious but less deadly than the preceding strains. Policy 3, considered less stringent, incurs lower economic and social costs than Policy 1 because it focuses on vulnerable groups rather than the entire population. Consequently, Policy 3 emerges as a preferable strategy when the dominant virus is highly transmissible (e.g., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{0}\u0026gt;5\\)\u003c/span\u003e\u003c/span\u003e) but poses less risk to those who are not vulnerable.\u003c/p\u003e\n\u003cp\u003eIt is noteworthy that enacting a policy immediately after the emergence of a highly transmissible virus (e.g., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{0}\u0026gt;10\\)\u003c/span\u003e\u003c/span\u003e) requires that the policy remains in place sufficiently long. Failing to do so could lead to a greater strain on the healthcare system (e.g., higher peak ICU occupancy and hospitalizations) than taking no action at all. This effect is especially marked with Policy 3 during the early and late Omicron outbreaks. For instance, as seen in Fig.\u0026nbsp;4, with the late Omicron variant, if Policy 3 is implemented just one-week post-outbreak, the peak ICU occupancy could surpass that of a no-policy scenario unless Policy 3 remains active for more than 14 days. This particular outcome does not extend to the metric of total deaths, indicating that while prematurely ending an NPI policy might increase healthcare system strain, it does not necessarily affect the total death count.\u003c/p\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003eThe Timing to Initiate an NPI policy\u003c/h2\u003e\n \u003cp\u003eIn practice, it is not feasible for a government to implement policies that restrict daily life for an extended period. The stricter the policy, the shorter the duration it can be sustained by the government. For instance, a Governor of a State in the United States can declare a state of emergency with the authority to enact certain measures, but only for a limited term. Therefore, we aim to investigate the optimal timing for implementing a policy, considering the constrained duration for which the policy can remain in effect. Figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e displays the peak ICU occupancy for the original virus strain under various policies, considering different durations of policy implementation. With the original virus strain, the stricter the policy, the lower the peak in ICU occupancy. For instance, a shelter-in-place policy (Policy 2) would most significantly reduce peak ICU occupancy compared to the other three policies. If it is feasible for a policy to remain in effect for an extended period, initiating the policy earlier is advantageous, as it tends to result in lower peak ICU occupancy. However, the trade-off is that a longer duration of policy implementation incurs higher economic and social costs.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e reveals that initiating a policy as early as possible is not the most effective strategy, unless the policy is maintained for a prolonged period (e.g., 84 days for Policy 1). There exists an optimal initiating time between Day 1 and Day 53 (the day ICU occupancy is projected to reach its peak without intervention). A shorter policy duration would shift the optimal initiating time to a later point. For example, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, if a policymaker can only enforce Policy 1 for two weeks (14 days), the optimal initiating time would be Day 43. Initiating Policy 1 any earlier than Day 43, with it lasting only 14 days, would lead to a higher peak in ICU occupancy.\u003c/p\u003e\n \u003cp\u003eA similar pattern is evident with other virus variants and metrics (e.g., peak infections, peak hospitalizations, and total deaths). When the prevailing virus strain is more transmissible, the optimal timing to initiate a policy for a specific duration moves to an earlier date. For example, as depicted in Fig. 4a, with the late Omicron variant, if a policymaker is limited to enforcing Policy 1 for only two weeks, the optimal initiating time would be Day 19, compared to Day 43 for the original virus strain (see Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eTotal deaths can serve as an indicator that prioritizes life-saving measures above economic and social costs. When examining Fig.\u0026nbsp;4a against Fig.\u0026nbsp;4b, it is evident that the best time to implement a policy varies between minimizing peak ICU occupancy and total deaths. For instance, in the scenario involving the late Omicron variant and a two-week enforcement of Policy 1, the optimal initiating day to minimize total deaths is Day 25, whereas it is Day 19 to minimize peak ICU occupancy. Initiating Policy 1 on Day 25 instead of Day 19 to minimize the total deaths necessitates an approximate 8% increase in the ICU capacity. This suggests that healthcare systems may need to endure a greater load to prevent more virus-related deaths. Such phenomenon is observed across all four policies and any given duration that the optimal initiating day of a policy to achieve the minimal total deaths consistently occurs later than that for minimizing peak ICU occupancy.\u003c/p\u003e\n \u003cp\u003ePolicymakers typically require some time to respond after the outbreak of a pandemic and are unable to maintain intervention policies indefinitely. Our findings offer encouraging insights for policymakers, suggesting that, to avoid overwhelming the healthcare system, there is no immediate need for action assuming the virus cannot be eradicated. Instead, it is optimal to delay the implementation of NPIs for a certain period. Nevertheless, if the dominant virus strain is highly transmissible, decision-makers must act more swiftly.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eResults of our study extend the understanding of policy effectiveness in the literature. For example, Ref.\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e studied the original virus and concluded that wearing mask should be widespread, rather than limited to susceptible or infectious individuals. Ref.\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e reviewed data from 32 countries with varying levels of policy strictness under the original virus and found that the higher the strength of government interventions at early stages, the more effective the policy was at reversing or slowing growth of death rate. Our results demonstrate that these are only true for the original virus but not for the more transmissible variants (e.g., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{0}\u0026gt;5\\)\u003c/span\u003e\u003c/span\u003e). The widespread masking policy is less effective, e.g., peak ICU, peak hospitalizations, and deaths than social distancing for the vulnerable group against Omicron.\u003c/p\u003e \u003cp\u003eIn Minnesota, the Governor started the Stay Home Order on 3/28/2020 when 441 cumulative confirmed cases and 5 cumulative deaths were recorded, and the order remained in effect until 5/18/2020, for a total of 54 days. Since the order was enacted on Day 7, i.e., 3/28/2020, our model\u0026rsquo;s results indicate that the best timing to end it should have been on Day 111 with a duration of 104 days, in terms of lowest possible peak ICU occupancy, or later than Day 150 in terms of the total deaths. The longest duration used in the numerical experiment is 150 days. The total deaths have not reached its lowest level on Day 150 if the Stay Home Order is enacted on Day 7. If the Governor was only able to keep the order in effect for 54 days, then the best timing to enact the Stay Home Order in Minnesota would have been on Day 28 to achieve the lowest peak ICU occupancy, or on Day 40 to minimize total deaths.\u003c/p\u003e \u003cp\u003eInterestingly, our model shows that if a policy is enacted on Day 7, kept for 54 days, with no other policies, the Stay Home Order (Policy 2) results in the highest total deaths (45.6K) by Day 365, compared to Policy 1 (44.5K), Policy 3 (37.7K), and Policy 4 (45.3K). Policy 2 also leads to the second highest peak ICU occupancy (5.0K), while Policy 1 results in 4.6K, Policy 3 in 4.5K, and Policy 4 in 5.1K. The best policy under these conditions is Policy 3 (social distancing for vulnerable groups), as it achieves the lowest peak ICU and total deaths, with lower social and economic costs. This suggests that stricter policies need to be in effect longer to be effective. If not, outcomes could be worse than with less strict policies, making the additional costs unjustified. The necessary duration of a policy shortens with increased virus transmissibility.\u003c/p\u003e \u003cp\u003eThe test-trace-quarantine policy is a suppression policy, which requires \u0026ldquo;high testing and tracing rates, high quarantine compliance, relatively short testing and tracing delays, and moderate to high mask use\u0026rdquo;\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. This policy aims to minimize the total infections rather than prevent the healthcare system from being overwhelmed. When effectively implemented, this approach can significantly reduce the transmission rate, potentially bringing it nearly to zero. According to Figure A1 in the Appendix III, if the strictest policy, with a 99% reduction of the contact rate (e.g., test-trace-quarantine policy), were enacted on Day 1 and lasted for 150 days, the peak ICU occupancy and the total number of deaths would almost be equivalent to the situation where no policies were used. This result suggests that such a strict policy cannot be lifted if the highly transmissible virus is not eradicated. Otherwise, the policy only delays the outbreak of the pandemic without reducing the total number of infections or deaths. Once lifted, the pandemic will begin anew. Thus, the test-trace-quarantine policy should be employed to buy time for the development of vaccines and effective treatments, or until the virus is eradicated.\u003c/p\u003e \u003cp\u003eCornell University is one example that successfully implemented this policy for as long as they could. Cornell University reopened for in-person instruction in Fall 2020, when the original virus was dominant, one of the earliest universities in the US to reopen during the pandemic. It implemented an asymptomatic screening program based on an SEIR model to test students regularly and test varsity athletes and students in Greek-life organizations even more frequently\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. Due to the specific settings of Cornell University, a near-closed community with a relatively small-scale total population, of which the majority is young and healthy; the compliance of this policy was high. Combining with mandatory vaccination, it succeeded in controlling campus outbreaks until Omicron hit in December 2021, which forced the university to shut down its campus\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. Cornell maintained their COVID restrictions as the New York State dropped its mask mandates in March 2022\u003csup\u003e12\u003c/sup\u003e. However, there was no severe illness in any of the infected students at Cornell since fall 2020\u003csup\u003e12\u003c/sup\u003e. From a 20/20 hindsight perspective, the number of infections might not be the best objective to determine NPI policies. Applying our results to the settings of Cornell University, the test-trace-quarantine policy might not be the most cost-effective strategy. We would recommend that Cornell University require social distancing for the vulnerable group only, particularly after the vaccine became available or when the virus was highly transmissible, e.g., Omicron, while imposing no restrictions for others.\u003c/p\u003e \u003cp\u003eChina is another example that implemented such a policy on a large scale, \u0026ldquo;dynamic Zero-COVID\u0026rdquo; policy, from January 2020 to January 8, 2023\u003csup\u003e44\u003c/sup\u003e. Due to the high compliance to the policy enforced by the government, it succeeded in keeping the number of COVID deaths low, about 6,000 deaths recorded among 1.4\u0026nbsp;billion people in China\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. According to our results, the suppression policy cannot be lifted until the virus is eradicated. China implemented the strictest policy early in the pandemic and maintained it for approximately three years, which allowed them to outlast the original and Delta variants. This approach ensured that the policy remained in effect long enough to achieve its intended goals. The country has, however, paid incredibly high social and economic costs, such as extremely harsh and severe restrictions on people's movements. This policy was no longer sustainable when Omicron hit.\u003c/p\u003e \u003cp\u003eAs the virus becomes more transmissible and less deadly, a better objective to manage the pandemic would be not to overwhelm the healthcare system rather than minimizing the infections. For example, if a policy is enacted on Day 7 under the late Omicron, our results show that Policy 3 needs to stay in place for 25 days to reach the lowest peak ICU occupancy of 4.2K a day and Policy 2 needs to stay in place for 30 days to reach the lowest peak ICU of 3.9K a day. Policy 3 is a good balance between the social costs and the burden on the healthcare system. Although the specific number cannot be directly translated into situations in China, the general conclusion applies to China, that Policy 3, social distancing for vulnerable groups, should be the best policy to use when Omicron was the dominant variant, rather than the strictest dynamic Zero-COVID policy.\u003c/p\u003e \u003cp\u003eThe optimal timing for initiating or terminating a policy is contingent upon the virus's transmissibility. There exists an ideal duration for a policy, beyond which no additional reduction in the peak burden on the healthcare system can be achieved. Note that extending an NPI beyond its ideal duration will continue to reduce overall infections and deaths. Lifting the policy after this period could cause ICU occupancy to rebound, but it would not exceed its previous peak level.\u003c/p\u003e \u003cp\u003eWith higher transmissibility of the virus, a shorter duration of the policy is required, necessitating a more rapid response time for decision-makers to implement an NPI policy. Should a stringent policy be implemented for a duration that is insufficient, its efficacy may be less than that of a less restrictive policy applied over the same period, potentially yielding outcomes worse than taking no action at all against a highly transmissible virus, e.g., Omicron.\u003c/p\u003e \u003cp\u003eFor a fixed duration of a policy, it is not always optimal to initiate the policy at the onset of the pandemic. The shorter the policy duration, the later it should be introduced into the pandemic timeline. Essentially, if a strict NPI policy like lockdowns cannot be sustained long enough, policymakers should not implement such stringent measures at the onset of a pandemic. Instead, policymakers should consider enacting these policies later in the pandemic for maximum effectiveness. This applies when virus eradication is infeasible, as with COVID-19\u003csup\u003e28\u003c/sup\u003e. If eradication is possible, most effective policy is a suppression strategy, such as test-trace-quarantine, as seen in the 2003 SARS outbreak\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. If suppression policy cannot be maintained until eradication or vaccines are available, we recommend switching to mitigation policies. Given that hospitalization, ICU admission, and mortality rates vary among different groups, optimal NPI policy should balance social costs and total deaths, targeting strategies based on the virus's transmissibility. For highly transmissible but less lethal variants (e.g., Omicron), social distancing for vulnerable groups is best. For less transmissible variants (e.g., the original virus, Delta, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{0}\u0026lt;5\\)\u003c/span\u003e\u003c/span\u003e), widespread masking is more effective. Modest social distancing is nearly ineffective against highly transmissible viruses.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eTo examine the balance between policy effectiveness and policy cost, we consider the following factors, including the virus variant, NPI policy, policy starting day, and policy duration (see Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). NPI policy refers to the four policies in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, each of which has different effectiveness in terms of the reduction to the transmission rate of a virus variant. The four NPI policies can be ordered by its strictness as Policy 2\u0026thinsp;\u0026gt;\u0026thinsp;Policy 1\u0026thinsp;\u0026gt;\u0026thinsp;Policy 3\u0026thinsp;\u0026gt;\u0026thinsp;Policy 4, where Policy 2 is the strictest. Policy starting day refers to the day that a policy is enacted, and Policy duration refers to how many days a policy is in effect.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eFactor and Level.\u003c/em\u003e We run the model with initial parameter settings (as in Table A1) without any intervention policies and the number of patients in ICU peaks at Day 53. Thus, we set 53 as the last meaningful day to start a policy.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFactor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLevels\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCOVID-19 variant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eoriginal virus, delta, early omicron, late omicron\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNPI Policy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1, 2, 3, 4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePolicy starting day\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1, 4, 7, \u0026hellip;, 53\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePolicy duration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1, 2, 3, \u0026hellip;, 150\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe COVID-19 virus variant includes the original virus (SARS-CoV-2), delta, early omicron, and late omicron. The original virus was first identified in China in December 2019 and arrived in the U.S. in early January 2020; the Delta variant was first detected in India in October 2020 and detected in the U.S. in February 2021; the early Omicron variant, e.g., BA.1, BA.2 was first detected in South Africa in November 2021 and in the U.S. in December 2021; the late omicron, e.g., BA.4 and BA.5 became dominant in the U.S. in June 2022\u003csup\u003e49\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e displays the estimated values of the major parameters of these variants that are used in this experimental study. According to the transmissibility, i.e., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{0}\\)\u003c/span\u003e\u003c/span\u003e of a virus variant, the four variants considered in the experiment are ordered as Late Omicron\u0026thinsp;\u0026gt;\u0026thinsp;Early Omicron\u0026thinsp;\u0026gt;\u0026thinsp;Delta\u0026thinsp;\u0026gt;\u0026thinsp;the original.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eEstimated Values of Major Parameter by COVID-19 Variants\u003c/em\u003e. The parameters for the original virus are calibrated using the COVID19 cases in Minnesota from March 23 through April 25, 2020, by Ref\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. The parameters of the other variants are obtained mainly from the CDC reports. The rate of hospitalized, the rate of ICU, and the rate of death are the average rates across all age group. We refer readers to the Appendix II for further details and data sources.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e COVID-19 variant\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{R}}_{0}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRate of Hospitalized\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRate of ICU\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRate of Death\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOriginal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0353\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2301\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0153\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDelta\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0796\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1765\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0123\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEarly Omicron\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0683\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1331\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0053\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLate Omicron\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0377\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0028\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe SEIR model and its extensions have been widely used to study infectious diseases, e.g.\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. We adopt the SEIR-type model used by the Minnesota government\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e to replicate the COVID-19 pandemic. The model (see Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e) extended the typical SEIR model by including multiple exposed states E, multiple asymptomatic (AI) and symptomatic (I) infectious states, a component H to capture the information of hospitalizations (non-ICU), a component ICU to capture the information of patients who are currently in ICUs, and a component D to capture the information of deaths. This model also includes population stratification and age-specific mixing patterns. We include the specific parameter settings in Appendix I and refer readers to\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e for more details of the model.\u003c/p\u003e \u003cp\u003eTo make a fair comparison, we use the same initial settings for all variants. On Day 0, there were 201 infectious cases, 26 were hospitalized, 6 were in the ICU, and no deaths. The total population is set to be 5.69\u0026nbsp;million.\u003c/p\u003e \u003cp\u003eNote that the parameters of all the virus variants are empirically estimated based on the reported hospital data. Thus, the parameters, such as death rate, and hospitalized rate of later variants, e.g., delta and omicron are already considered the background immunity level, either from the earlier infection or the vaccinations in the population.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCOVID-19 virus is unlikely to be eradicated and we are more likely to live with it\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. Thus, rather than focusing on the total number of infections, hospitalizations, and deaths, our study focuses on the burden on healthcare resources, e.g., ICU beds due to COVID-19 virus. Infectious diseases should be managed to ensure that healthcare capacity is not exceeded, allowing individuals to receive the quality of care necessary to avoid unnecessary suffering or deaths. Thus, this paper uses the following criteria to evaluate the effectiveness of a given policy, the number of patients being hospitalized at a given day, and the number of COVID-19 patients being in ICU at a given day, and the total deaths, where the first two reflects the burden on the healthcare system and the last one reflects the ultimate severity and impact of the disease on the population.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAuthor contributions statement\u003c/p\u003e\n\u003cp\u003eC.X., S.K. and Y.M. conceptualized and designed the study, worked on curation of data, and contributed to the interpretation of results. C.X., and Y.M. drafted the manuscript. N.G., and C.C. worked on curation of data, worked on interpretation of results, and revision of the manuscript. All authors have read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eThere was no funding for this research.\u003c/p\u003e\n\u003cp\u003eCompeting interests\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003eData availability\u003c/p\u003e\n\u003cp\u003eAll data generated or analysed during this study are included in this published article [and its supplementary information files]\u003c/p\u003e\n\u003cp\u003eAdditional information\u003c/p\u003e\n\u003cp\u003eSupplementary information is provided in Appendix I and Appendix II.\u003c/p\u003e\n\u003cp\u003eCorrespondence and requests for materials should be addressed to C.C.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAyouni, I. et al. 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PMID: 35712857; PMCID: PMC9196831.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4511189/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4511189/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNon-pharmaceutical intervention (NPI) policies, ranging from mild intervention to total isolation, were implemented during the COVID-19 pandemic across the globe. We adopt a systematic approach to guide policymakers in deployment of NPI policies to mitigate the pandemic's effects while maintaining a proper balance on their social and economic impacts. The optimal timings to enact and to end a policy depend both on the strictness of the policy and the transmissibility of the virus. Our results show that the strict policy is not always the most effective to mitigate the disease, while other modest NPIs can function better especially when the virus is highly transmissible. If an NPI can only be applied for a limited period due to economic and social constraints, it is always suboptimal to implement it at the pandemic's onset.\u003c/p\u003e","manuscriptTitle":"From Node to Network: Weaving A Global Perspective on Efficacy and Costs of Non-Pharmaceutical Interventions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-31 13:17:35","doi":"10.21203/rs.3.rs-4511189/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-10-24T20:17:09+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-24T15:08:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"195813112685324644632011326876986189121","date":"2024-10-13T14:31:30+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-24T20:39:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"62475596854363582952774787724046559300","date":"2024-08-05T15:25:52+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"251835220176296073671863808773735055406","date":"2024-08-04T15:11:48+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-07-21T04:25:46+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-21T04:22:22+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-07-11T13:56:08+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-08T09:48:50+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-05-31T22:23:40+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4a40beeb-c2f3-4d2e-a5ac-ff9cbea90be0","owner":[],"postedDate":"July 31st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":35151236,"name":"Health sciences/Diseases/Infectious diseases/Influenza virus"},{"id":35151237,"name":"Biological sciences/Immunology/Infection"}],"tags":[],"updatedAt":"2025-01-27T16:07:36+00:00","versionOfRecord":{"articleIdentity":"rs-4511189","link":"https://doi.org/10.1038/s41598-025-87566-8","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-01-22 15:58:16","publishedOnDateReadable":"January 22nd, 2025"},"versionCreatedAt":"2024-07-31 13:17:35","video":"","vorDoi":"10.1038/s41598-025-87566-8","vorDoiUrl":"https://doi.org/10.1038/s41598-025-87566-8","workflowStages":[]},"version":"v1","identity":"rs-4511189","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4511189","identity":"rs-4511189","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}