key: cord-337516-hrcf2udq
authors: Dickens, Borame L.; Koo, Joel R.; Lim, Jue Tao; Park, Minah; Quaye, Sharon; Sun, Haoyang; Sun, Yinxiaohe; Pung, Rachael; Wilder-Smith, Annelies; Chai, Louis Yi Ann; Lee, Vernon J.; Cook, Alex R.
title: Modelling lockdown and exit strategies for COVID-19 in Singapore
date: 2020-08-01
journal: nan
DOI: 10.1016/j.lanwpc.2020.100004
sha: 
doc_id: 337516
cord_uid: hrcf2udq

Abstract Background With at least 94 countries undergoing or exiting lockdowns for contact suppression to control the COVID-19 outbreak, sustainable and public health-driven exit strategies are required. Here we explore the impact of lockdown and exit strategies in Singapore for immediate planning. Methods We use an agent-based model to examine the impacts of epidemic control over 480 days. A limited control baseline of case isolation and household member quarantining is used. We measure the impact of lockdown duration and start date on final infection attack sizes. We then apply a 3-month gradual exit strategy, immediately re-opening schools and easing workplace distancing measures, and compare this to long-term social distancing measures. Findings At baseline, we estimated 815 400 total infections (21.6% of the population). Early lockdown at 5 weeks with no exit strategy averted 18 500 (2.27% of baseline averted), 21 300 (2.61%) and 22 400 (2.75%) infections for 6, 8 and 9-week lockdown durations. Using the exit strategy averted a corresponding 114 700, 121 700 and 126 000 total cases, representing 12.07–13.06% of the total epidemic size under baseline. This diminishes to 9 900–11 300 for a late 8-week start time. Long-term social distancing at 6 and 8-week durations are viable but less effective. Interpretation Gradual release exit strategies are critical to maintain epidemic suppression under a new normal. We present final infection attack sizes assuming the ongoing importation of cases, which require preparation for a potential second epidemic wave due to ongoing epidemics elsewhere. Funding Singapore Ministry of Health, Singapore Population Health Improvement Centre.

case importation and the non-elimination of local cases, which parallel economic and social issues from lockdown implementation. Sustainable and public-health orientated exit strategies are therefore required. We searched PubMed from database inception to May 20, 2020, for articles using the search terms "COVID-19", "SARS-CoV-2", "Exit Strategies" "Lockdown" and "Control Measures". Our search yielded three modelling papers of relevance. Two articles examined control strategies within Wuhan with one focusing on the effects of social mixing and the other on case isolation. Another estimated the efficacy of long-term social distancing in the US. We found no articles which modelled the impacts of national lockdown and exit strategies for countries within the Western Pacific outside of China.

In response to the rising number of local coronavirus disease 2019 (COVID-19) cases, many countries have implemented lockdowns to restrict movement and community interactions and thereby suppress infection. Details vary [1] but measures commonly include the closure of premises such as non-essential workplaces, schools, recreational facilities and places of worship. Essential services in healthcare, transport, cleaning, food services and supply chains may remain open to sustain the economy and welfare of the population. Most lockdowns have successfully reduced the reproduction number and curtailed epidemic growth, but emerging from a lockdown prematurely without sufficient planning may result in epidemic rebounding [2] , as the previous suppression of cases may leave a substantial proportion of the population susceptible to infection. Intermittent lockdowns have been proposed [3] through the cycling of initiation and cessation of these interventions-possibly until 2022-to avoid exceeding hospital capacities. Concerns exist, however, on the long-term economic disruption, negative consequences on social and mental well-being, and costly administration required to ensure compliance.

Here, in the context of lockdown and social distancing measures, we explore the impact of a gradual release exit strategy (GRES) with a rollback of social distancing interventions operating outside of trigger mechanisms from emergency intermittent lockdown measures. Health and isolation facility expansion and preparation will be required during the lockdown phase regardless of control strategy to maintain a high standard of healthcare, which can substantially reduce case fatality rates [4] . GRES can provide timelines to government agencies, services and businesses, and allow society and the economy to return to a new-normal state with continuing extensive education on the importance of safe distancing, hygiene practices and precautionary measures such as mask wearing. We assess GRES through an agent-based model of a city, modelled upon the city-state of Singapore.

The implementation of social distancing measures in Singapore has been progressive from 10 March with the rollout of gradually stricter recommendations and regulations [5] , leading to the implementation of a 'circuit breaker' [6] , or lockdown, on 7 April 2020 in response to rising autochthonous cases. Although Singapore's lockdown seemingly had no effect on several large outbreaks among foreign worker dormitories that started in early April, it appears to have arrested the epidemic growth in the general population, using school closures and workplace distancing as recognized and effective attack rate reduction measures [ 7 , 8 ] . Substantial education and productivity losses are expected with all children tele-learning and an estimated 80% non-essential employees working from home or unable to work [9] . In response, a 3-tier financial support package for businesses and individuals has been released to provide financial assistance for families, support networks, workers and students amounting to ∼$38.8 billion USD [10] . On 21 April 2020, the Singaporean Government announced an extension of social distancing measures to 8 weeks in total with plans to end on 1 June 2020 [11] .

We utilise the geographical, demographic and epidemiological model of Singapore for respiratory diseases (GeoDEMOS-R), an agent-based epidemic simulation model comprising of a synthetic and calibrated population where the impact of interventions can be measured. The model has been previously used to estimate the effects of early epidemic control [12] and of home versus institutional isolation of cases [13] , and has been updated and expanded to assess exit strategies. In summary, we investigate the effects of early social distancing, lockdown and GRES in 480 days by:

(1) Establishing a limited control baseline with case isolation and quarantining of family members only; (2) Measuring the impact of 6-week (early cessation), 8-week (planned) and 9-week (extended) lockdown in duration, at different start dates of 5, 6, 7 and 8 weeks, on the final infection attack size, when compared to a no-exit strategy where lockdown is immediately lifted; (3) Estimating the effects of this lockdown with GRES which includes the immediate re-opening of schools post lockdown, due to their limited epidemic suppression impact [14] , with a 3-month readjustment period. In the first 2 months, 50% of the workforce returns physically to work, followed by 1 month at 75%, before full re-opening to pre-epidemic levels; and (4) Comparing lockdown to a no-lockdown strategy with longterm social distancing of differing start times at 5, 6, 7 and 8 weeks from the epidemic start date and durations of 2, 4, 6 and 8 weeks. During this period, 50% of the adult population is actively working, schools are closed and active social distancing is being done within the community.

The model used is GeoDEMOS-R, an agent-based epidemiological model with a synthetic resident population that is heavily calibrated to be representative. Full details are explained elsewhere; [12] here we provide a summary. Households were constructed using 178 census tables based on a sample of 20 0,0 0 0 households. An heuristic search algorithm was used to create a total of 3.77 million Singaporeans with the attributes of age, ethnicity and gender. Remaining attributes were drawn randomly from the specified attribute's marginal distribution and summary tables of the population comparable to the census tables formed whose fit were assessed using Pearson's chi-squared statistic. Zero count cells were avoided by setting them to 0.1. Each attribute was fitted using a Monte Carlo swapping algorithm, which swaps two random individuals' data until the improvement in fit becomes negligible ( < 0.001% improvement for 10,0 0 0 runs). The same process was used to generate partners, allocate children and create multi-generational families for 1.14 million households. Households were geolocated within discrete areas named subzones according to spatial characteristics outlined in the census, and individuals allocated workplaces and schools appropriately based on distributions of commuting time data from Singapore's Household Inter- view Travel Study and EZ-Link data which is a 1-month record of the majority of the population's public transport activities.

In the transmission model, day and night steps exist to differentiate movement behaviour and infection likelihood between individuals within the household, school, workplace and community. During the day, workers interacted with individuals in the same workgroup, and students within their classes. These two groups also interacted with those in the wider area around their workplace and school at community rates. Individuals who were not working or studying were modelled to interact with people in the same residential community. In the night step, individuals interacted primarily within their households where children had the highest probability of contact with his or her family members.

Suppose i and j are two individuals in the synthetic population with j becoming infected, we denote the probability of j infecting i on day t in location type g as

(1)

Here β g is constant for location type g , defined as the home, workplace or school which both individuals belong to; β g is obtained from a contact rate study (Supplementary Table 1 , 2) for different social group settings in Singapore where the contact rates serve as the likelihood for individuals to infect one another at specific group locations and the wider spatial subzone area.

Overall, the probability of individual i getting infected from location type g on day t is therefore given as,

Here G is a set of individuals of location type g, G t is the subset of all individuals who belongs to set G and are infectious on day t . We use | . | to denote the size of the set of individuals. Hence, | G | is the total number of people in set G . The number of people in set G that would be infected on day t can be denoted by a random variable X G ( t ) and

where G r is the subset of G consisting of individuals that have been removed through hospitalisation and subsequent recovery. The total number of people α infected on day t can then be expressed by summing over all the different sets of individuals in the population,

For each simulation, the model was run for 480 daysapproximately 15 months-to estimate the number of cases by the end of April 2021; cases began entering Singapore in January 2020.

With more epidemiological information available, model parameters that were previously based on the severe acute respiratory syndrome coronavirus (SARS-CoV) have been updated (a summary of parameters and interventions is provided in Supplementary Table 1 ). We assumed that the basic reproductive number ( R 0 ) for SARS-CoV-2 was 2.0 [15] , the asymptomatic rate was 17.9% [16] and the incubation cumulative distribution function was modified to have a median incubation period of 4 days [17] .

The R 0 parameter was built with a multiplier γ , which modified the infectiousness parameter of each individual in the simulation [18] . We first simulate the initial 4 weeks for a selected γ ∈ [0, 1]. This γ has a correspondence with r ∈ R , the value of the exponential model exp( rt + b 0 ) that best fits the simulated 4-week outbreak. This value of r was used in the linearized form of the susceptible-exposed-infectious-removed (SEIR) model [19] to compute the corresponding R 0 . Through this process we obtained a corresponding value of R 0 for γ . A grid search was performed on γ , with γ that corresponded closest to R 0 = 2.0 being selected.

For each scenario, we had case importation based on a Poisson model with λ = 2.0. To calculate λ, case importation data was used to fit a model on the expected number of daily case importations, where λ was the model's average case importation over time.

For this study, we ran 100 simulations for each intervention. There was no limit to isolation capacity as we assumed that the majority of the symptomatic cases will be transferred to hospital or community isolation facilities. Our baseline scenario included the isolation of ascertained cases and home quarantine of their household members. All ascertained cases are assumed to have a 24-h delay before they are no longer infectious to the wider population to accommodate for healthcare facility visitation and testing. We additionally assumed perfect compliance of those under household quarantine as strict punitive measures are in place.

For lockdown, a harsher penalisation on the contact rate was implemented with an initial 2-week period of social distancing, followed by a 6, 8 or 9-week period where schools remained closed, and work and community contact rates are further reduced to 20%. This further reduction is to simulate essential work and economic activity still being carried out by the population during the lockdown period. The starting points were at week 5, 6, 7 and 8 of the epidemic.

For the post lockdown strategy, two scenarios were modelled. The first assumed conditions went back to a pre-epidemic state with all schools, workplaces and the community at 100% transmission. The second, labelled as the gradual release exit strategy (GRES), assumed a successive restoration of contact rates over a period of three months. In the two months directly after lockdown, schools reopen and contact levels are restored at 50%, followed by 1 month of 75% restoration of workplace and community contact levels, and then pre-epidemic contact rates at 100%. This represents a cautious and planned approach to avoid heavily abnormal contact disruption from the initial lockdown period whilst maintaining a level of epidemic suppression.

For a long-term social distancing strategy, school closure occurs and we assume 50% suppression in contact rates at workplaces and within the wider community. This measure can begin at week 5, 6, 7 and 8 where at each starting point, social distancing was implemented for 2, 4, 6 and 8 weeks in duration. After the end of the social distancing period, all schools were reopened with contacts restored to pre-intervention levels. The two weeks of social distancing pre lock-down are also assumed to follow the same contact rate reduction levels with school closure.

We present the main results using a 17.9% asymptomatic proportion, and the same analysis for 44% in the Supplementary Information ( Supplementary Figs. 1-4) .

For the limited control baseline, the total number of infections by 480 days was 815 40 0 (IQR: 814 60 0-816 50 0), which represents 21.62% (21.60-21.65%) of the total population ( Table 1 ) A delayed post lockdown secondary peak size of 6060 (5260-6740) daily cases occurs for a 6-week lockdown duration starting at week 7, which is reduced further to 5890 (5040-6590) for an 8week lockdown in duration ( Fig. 1 (e) ). Whilst substantially lower than the baseline peak, the initial pre-lockdown peak is relatively high. This peak is suppressed however for a lockdown starting at week 6 ( Fig. 1 (c) ). Although the secondary peak is greater at 14 100 (13 200-15 000) and 13 900 (12 800-14 700) daily cases respectively, it represents peak suppression throughout the epidemic in comparison to the baseline.

Lockdown start time has a larger impact than duration as relatively small ranges in the cases averted exist; For an asymptomatic rate of 44%, the total number of infections by 480 days rose to 1 085 0 0 0 (1 084 0 0 0-1 086 0 0 0), representing a 24.9% increase in the infected population.

For lockdown and GRES, early lockdown at 5-weeks had a final infection attack size of 700 700 (699 000-702 800) total cases for a 6-week lockdown, 693 700 (691 000-695 700) for 8-week lockdown, and 689 400 (686 80 0-692 20 0) for a 9-week lockdown ( Table 1 ) Lockdown start time has a large impact on GRES ( Fig. 1 and Table 1 ). With early lockdown implementation at 5 weeks, when compared to no-exit strategy, GRES averts an average of 96 200 cases (12.07%) in total for a 6-week early cessation lockdown, 100 400 (12.64%) for the planned 8-week and 103 600 (13.06%) for the prolonged 9-week. At this 5-week start time, GRES also reduces the secondary peak size by 9 900 (46.92%), 10 100 (49.03%) and 10 200 (50.25%) at a ∼28-day delay respectively ( Fig. 1 (a) ). If implemented later and close to the epidemic peak at week 8, the efficacy of GRES diminishes with 11 300 (1.91%), 10 600 (1.81%) and 9900 (1.69%) cases averted in total, with no determinable sec- ondary peak ( Fig. 1 ) . GRES' lessening utility with later lockdown start times is due to a large proportion of cases having already occurred in the first half of the epidemic. Post lockdown peak sizes for a 6 week start time lockdown strategy are substantially reduced with 8740 (8580-8980), 8760 (8590-8930) and 8850 (8650-8980) daily cases for a 6, 8 and 9week duration lockdown with GRES and 14 100 (13 20 0-15 0 0 0), 13 900 (12 800-14 700) and 13 800 (12 800-14 700), respectively, without ( Table 1 ) . This represents a 38.01, 36.98% and 35.87% reduction. For an earlier implementation lockdown time at 5 weeks, a 47.92%, 49.03% and 50.25% corresponding post lockdown peak reduction is observed.

Lockdown duration had a limited impact on GRES, acting as a suppressive, not a preventative, measure. When utilising the 6week early cessation, planned 8-week lockdown and prolonged 9week lockdown, a difference of 89 10 0, 94 0 0 0 and 98 300 cases can be averted across the different start dates of 5, 6, 7 and 8 weeks using GRES in comparison to lockdown alone; differing only by 9200 cases between these duration times.

At a greater asymptomatic proportion of 44% we observed similar outcomes in terms of cumulative infection numbers for lockdown implementation on week 5 and 6 (Supplementary Figs. 1 and 2) although it represented an overall accelerated epidemic. The largest difference was observed for a 6-week lockdown with GRES at week 5 where 833 600 (827 700-837 400) infections were observed in comparison to 700 700 (699 000-702 800) at an 17.9% asymptomatic rate.

Long term social distancing at durations of 2, 4, 6 and 8-weeks cause resulting final infection attack sizes of 820 100 (818 500-821 40 0), 804 90 0 (801 30 0-808 0 0 0), 783 60 0 (779 0 0 0-786 30 0) and 759 0 0 0 (753 80 0-763 0 0 0) total cases across implementation start times of 5, 6, 7 and 8 weeks ( Table 2 ) . Post social distancing peak sizes show suppression, particularly for implementation times of week 7, although if implemented at week 6, the initial peak is also reduced ( Fig. 2 ) .

The secondary peaks caused by early lockdown and GRES are comparable to long-term social distancing with 50% activity in the community and the workplace, wherein 6-week interventions starting at week 7 cause a maximum of 5390 (4750-6070) cases for the former and 5490 (4710-6040) cases in the latter ( Fig. 2 (e) ). Long term social distancing is less effective at durations of 4 weeks or lower, averting up to 1.29% of cases relative to the baseline for an implementation time at 5 weeks ( Table 2 ) . For a duration of two weeks in social distancing, a maximum of 11.22% of cases relative to the baseline can be averted if implemented close to the epidemic peak at 8 weeks.

For longer durations of 6 to 8 weeks, 3.90-6.92%, 9.59-12.84%, 17.27-20.25% and 25.59-28.48% of cases can be averted relative to the baseline for start dates of 5, 6, 7 and 8 weeks respectively. For a week 6 implementation time, 12.84% of cases can be averted 

Critical uncertainties lie ahead on moving forward during lockdown periods in when and how to release the population back to a new normal state. Our findings suggest that earlier lockdown requires a GRES to prevent a large secondary peak, which becomes

JID: LANWPC [m5G; August 1, 2020; 13:30 ] less important the later the lockdown is implemented. As Singapore entered lockdown relatively early where ∼100 cases were being reported daily, a lockdown with no exit strategy could result in up to 796 900 (791 800-799 300) total cases across 480 days, which averts 2.27% of cases in comparison to the baseline. GRES can avert up to 14% of cases for the same scenario. For lockdowns implemented at later weeks, substantial proportions of cases are averted, as observed for other epidemics [20] , with a final infection attack size of 591 500 (577 80 0-60 0 10 0) at week 8 as an example, although this will not be viable for most countries where their healthcare capacity cannot cope with large, early epidemic peaks. When GRES is compared with no exit strategy for a 5 and 6week implementation start time, it results in a reduction of 8.01-13.06% in final infection attack size, and 0.78-1.91% reduction for a 7 and 8 week start time as a large proportion of cases have already occurred in the initial epidemic ramp up. GRES therefore shows good utility in populations where substantial proportions are susceptible to infection, reducing the overall outbreak size and slowing down infection spread with a greater number of transmission events prevented. This may provide opportunity to introduce prophylaxis or vaccination measures in the future, or allow the implementation of mandatory testing of all incoming travellers, which can prevent these infection events from occurring altogether as the epidemic dies out. This is especially paramount as the number of cases beyond 365 days, although considerably lower than the initial peaks, still ranges from 6.51-513.21 cases per day for GRES strategies (Supplementary Table 3a ) and 4.94-90.03 for long term social distancing strategies (Supplementary Table 3b ) with the ongoing risk of secondary case spread from imported cases. At the start of the epidemic however, the duration of lockdown has a limited impact on the efficacy of GRES in terms of final infection attack size, which suggests that the period should be used for epidemic preparation rather than an ongoing control method, although an extended lockdown of 8 or 9 weeks will avert more cases.

Should medical capacity permit, long term social distancing remains a viable strategy provided it is carried out for a duration of at least 6 weeks with 50% of the population working and schools closed. The total infection attack size is less for social distancing relative to lockdown with no exit strategy, but remains greater than GRES which is the most effective strategy. For overall peak size minimization, both a social distancing and GRES implementation time of 6 weeks is optimal, although if earlier lockdowns or social distancing measures have been implemented, GRES is essential for peak reduction. With a greater asymptomatic rate of 44%, the epidemic is considerably accelerated requiring earlier intervention at 4 or 5 weeks to slow infection spread. GRES remains effective at a 23.1% reduction in the final infection attack size in comparison to the baseline although these implementation dates are notably much later into the epidemic in comparison to the 17.9% asymptomatic proportion findings.

Multiple complexities exist in the framing of exit strategies to the public, including the attribution of accountability among policymakers and individuals, the acceptance of uncertain economic burdens, and need for flexibility as technologies emerge and other countries respond differently as the epidemic progresses. Lockdown and GRES can maintain public preparation, awareness and adherence which may abate if complete cessation and re-initiation of measures are introduced for extensively long periods, as observed generally for long-term therapies and lifestyle changes [21] . The strategy also partially mitigates isolation fatigue and social disruption, and should be conducted along with case finding, contacttracing and quarantining, mass-testing in key groups such as those working with vulnerable populations, and serological surveys. With GRES in place, which will still require healthcare system ramp-up, real-time forecasting efforts can also continue to estimate appro-priate intervention trigger times should another lockdown be required. Investment into the healthcare system to accommodate for the caseloads estimated in the study could avoid recurrent lockdowns, if the healthcare system can cope with the number of severe cases.

The prolonged flattening, not elimination, of the epidemic across scenarios is due to the constant influx of a conservative 2 estimated imported cases per day at the global travel hub, an estimated 17.9% (or 44%) prevalence of asymptomatic infections and inevitable future relaxation of travel restrictions to allow for influxes of short and long-term worker immigration. Additionally, containment measures and lockdowns vary widely in duration and severity between countries, [1] causing differing and delayed epidemic peaks among source countries, making lockdown a temporary protection measure against highly uncertain external epidemiological forces where delays in reactive control measures abroad or within Singapore will result in inevitable national case spread. Although seroprevalence data has yet to be released, due to the ongoing lockdown measures, a substantial proportion of the population is suspected of being susceptible to infection, which exacerbates the effects of case importation.

Ongoing concerns regarding the effects of school closure remain at the forefront of COVID-19 control policy. GRES prioritises school re-opening as clinical manifestations of children's COVID-19 appear generally less severe [22] . The societal impacts of school closure among young children, working adult parents and older children in terms of productivity and education loss are likely to be extensive and unsustainable. With continued school closure, socioeconomic inequalities will be further exacerbated, despite governmental intervention to provide intensive distance learning for all school children [23] . Overall, outside of education, schools operate as a safety net for at-risk children, providing nutritional, emotional and social support as well as vaccinations and development opportunities.

Limitations of this study include uncertainties on the current number of infections, which could not be used directly to validate the initial phase of the epidemic in the agent-based model. Parameter estimations from larger global studies were therefore used to simulate epidemics although wide ranges in observations continue to be reported for parameters such as asymptomatic rates. The model can be calibrated in the future with real time forecasting effort s and result s of serology surveys to better reflect COVID-19 prevalence and incidence within Singapore. Intra workplace and school contact patterns were additionally not accounted for, which may cause greater or fewer localized contact events depending on internal grouping structures.

Further uncertainties include the current and future adherence to social distancing measures, future importation rates and spatial heterogeneities in infection rates. Ongoing epidemics in high density accommodation (Supplementary Figure 5) and their effects in the wider community were also not accounted for, which requires further investigation.

BLD and JRK performed the modelling and wrote the manuscript. BLD, JRK, VJL and ARC designed the intervention strategies. MP and SQ performed data collection. JTL, HS, YS, RP, AWS, LYAC, VJL and ARC critically revised the manuscript.

The study sponsors had no role in the study design, analysis, interpretation of the data or writing of the report.

LANWPC [m5G

First-wave COVID-19 transmissibility and severity in China outside Hubei after control measures, and second-wave scenario planning: a modelling impact assessment

Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period

How will country-based mitigation measures influence the course of the COVID-19 epidemic

Past updates on COVID-19 local situation

COVID-19 (Temporary Measures) Act 2020. Singapore: Republic of Singapore, Thursday

The effect of school closure on hand, foot, and mouth disease transmission in Singapore: a modeling approach

Effectiveness of workplace social distancing measures in reducing influenza transmission: a systematic review

Strong national push to stem spread of COVID-19

Interventions to mitigate early spread of SARS-CoV-2 in Singapore: a modelling study

Institutional, not home-based, isolation could contain the COVID-19 outbreak

School closure and management practices during coronavirus outbreaks including COVID-19: a rapid systematic review

Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia

Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship

Investigation of three clusters of COVID-19 in Singapore: implications for surveillance and response measures

FluTE, a publicly available stochastic influenza epidemic simulation model

Comparative estimation of the reproduction number for pandemic influenza from daily case notification data

Strategies for mitigating an influenza pandemic

Long-term adherence to health behavior change

Epidemiology of COVID-19 among children in China

Mitigate the effects of home confinement on children during the COVID-19 outbreak

The authors declare no competing interests.

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.lanwpc.2020.10 0 0 04 .

All data used within the study is publicly available. GeoDEMOS-R data is available on request.