A Study on The Effectiveness of Lock-down Measures to Control The Spread of COVID-19
Subhas Kumar Ghosh, Sachchit Ghosh, Sai Shanmukha Narumanchi
AA Study on The Effectiveness of Lock-downMeasures to Control The Spread of COVID-19
Subhas Kumar Ghosh , Sachchit Ghosh , and Sai Shanmukha Narumanchi Commonwealth Bank of Australia, Sydney, New South Wales, 2000, Australia The University of Sydney, Camperdown, NSW 2006, Australia Department of Computer Science, Southern Illinois University, Carbondale, IL 62901, USA a [email protected] ABSTRACT
The ongoing pandemic of coronavirus disease 2019-2020 (COVID-19) is caused by Severe Acute Respiratory SyndromeCoronavirus 2 (SARS-CoV-2). This pathogenic virus is able to spread asymptotically during its incubation stage through avulnerable population. Given the state of healthcare, policymakers were urged to contain the spread of infection, minimizestress on the health systems and ensure public safety. Most effective tool that was at their disposal was to close non-essentialbusiness and issue a stay home order. In this paper we consider techniques to measure the effectiveness of stringencymeasures adopted by governments across the world. Analyzing effectiveness of control measures like lock-down allows usto understand whether the decisions made were optimal and resulted in a reduction of burden on the healthcare system. Inspecific we consider using a synthetic control to construct alternative scenarios and understand what would have been theeffect on health if less stringent measures were adopted. We present analysis for The State of New York, United States, Italyand The Indian capital city Delhi and show how lock-down measures has helped and what the counterfactual scenarios wouldhave been in comparison to the current state of affairs. We show that in The State of New York the number of deaths couldhave been 6 times higher, and in Italy, the number of deaths could have been 3 times higher by 26th of June, 2020.
Introduction
In December 2019, an outbreak occurred in Wuhan, China involving a zoonotic coronavirus, similar to the SARS coronavirusand MERS coronavirus . The virus has been named Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), andthe disease caused by the virus has been named the coronavirus disease 2019 (COVID-19). Since then the ongoing pandemichas infected more than 9 million people and has caused more than 467 thousand deaths worldwide. Since the initial outbreak,several different studies have tried to estimate the number of infections that stem from a single infected patient in order topredict the potential for transmission of the COVID-19 virus. In most cases, it was seen that R >
1, implying exponentialgrowth through infection of a vulnerable population. Original estimates placed mortality rates for individuals at high risk at4.46 % with those suffering from cardiovascular or kidney disease having even greater susceptibility . The SARS-CoV-2 virushas no available treatment as the pathways for proliferation and pathogenesis are still unclear . Current treatments are based onthose effective on strains of the previous SARS coronavirus and MERS coronavirus. The SARS-CoV-2 virus is able to replicaterapidly during the asymptomatic phase and affect the lungs and respiratory tract, resulting in pneumonia, hypoxia, and acuterespiratory distress . Infected patients are directly dependent on external ventilation in most cases.With the increasing pressure on the health systems due to reliance on intensive care units or non-invasive ventilation, healthstrategies were required to be implemented. The concern was to ensure the number of infected patients does not exceed thehealth system’s ability to cope with it. It also focused on increasing the capacities of available health systems at the time. Underthe conditions at the time, with a highly pathogenic SARS-CoV-2 that is able to spread asymptotically during its incubationstage through a vulnerable population, policymakers were urged to contain the spread of the infection, and minimize stress onthe health systems and ensure public safety. This was done by issuing orders for widespread lock-down and implementingsocial distancing measures. All non-essential businesses and services were shut down until further notice.Taking measures to reduce stress on the health sector and diminishing the number of infected patients is important to endthe pandemic, and understanding the effectiveness of a lock-down enables the distinction of good safety measures from badones. Analyzing effectiveness of control measures like lock-down allows us to understand whether the decisions made wereoptimal and resulted in a reduction of burden on the healthcare system, and broke chain of transmission, preventing its spreadand reducing the reproductive rate of the virus. Any optimal policy considers a trade off between the benefit associated withlock-down and cost of reduced aggregate output. Aggregate output decreases as a function of the stringency of the policy,commitment from the government to maintain the level of stringency and adherence of general population. Aggregate output a r X i v : . [ phy s i c s . s o c - ph ] A ug ecreases through lower supply of labor, lower consumption and hence through lower investment, which results from investors’expectation of a lower marginal product of capital. On the other hand benefit associated with lock-down can be seen throughthe number of lives potentially saved and in curbing the pandemic early so that economic activity can be restarted early.Our objective in this work is to understand the benefits obtained from stringency measures adopted by governments acrossthe world in terms of its health benefits. In the remaining of this section we describe our contribution and related works.Subsequently in Section we provide a brief overview and mathematical underpinning of the tools that we use and describe ourdata driven methodology and in Section we present our results in three different geographic setup. Finally, in Section wepresent some concluding remarks. Our contribution
In this work we consider stringency measures adopted by governments across the world and provide a counterfactual assessmentof the benefit from those measures in terms of health benefits. In order to estimate the counterfactual metric (say number ofdeaths), we use a geographic location as a treatment unit (say Italy) and a set of other geographic locations as donor group (sayBrazil and United States). We take a data driven approach to construct a synthetic control using pre-intervention perioddata (say from early February, 2020 to March 9, 2020) of the donor units and their linear combination, such that the squarederror between the estimated synthetic control and the treatment unit is minimized by the choice of weight parameters in thispre-intervention time period. Now synthetic control can be extrapolated to estimate the metric. We use Multi-dimensionalRobust Synthetic Control (m-RSC) as a tool as described in .However, there are few difficulties in applying the tool as it is. Firstly, different governments adopted different levels ofstringency measures and there were different levels of compliance, and commitment. Secondly, there were no ‘pure‘ donorgroups as stringency measures were nearly ubiquitous. So we have used various secondary sources of data to score the level ofstringency measures , and level of compliance. This allowed us to determine donor groups relative to a choice of treatment unit.Finally, we present our results in three different geographic setup - namely in the State of New York, Italy and Indian city ofDelhi, and analyze them. Related Works In , authors have shown that the reproductive rate of the SARS-CoV-2 had significantly decreased after government intervention.They show that the spread of disease was confined if measures were brought into effect early. In , authors use the differentialtiming of the introduction of stringency measures and changes in Google searches for unemployment claims to establish aframework to estimate how each stringency measure contributes to unemployment. Authors show that early intervention effortsin the form of non-essential business closure have contributed to less than 8.5 percent of unemployment claims.Another facet to measure the success of the lock-down is to observe its effects on the health systems. Late intervention inthe case of Italy led to the flooding of hospitals and ICUs due to exponential spread. However, the national lock-down waseffective in reducing the proliferation and decreased the stress on the national health system as observed by authors in . Intheir paper , authors extend the SIR model to include auxiliary state variables in the form of hospital capacity, contact withan infected person, etc. They use a system dynamics model of the outbreak to simulate various lock-down scenarios withrecommendations for optimal strategy. In our work we consider the possible outcome if such strategies were not adopted, andpresent counterfactual scenarios.International travel has also been impacted as a result of efforts to reduce the spread of the coronavirus disease. On the basisof reported cases, models built by show a significant decrease in the number of infections compared to predictions if no travelbans were adopted as an option. Their modeling results indicate that travel restriction must be combined with a transmissionwithin the community to curb the spread. Results
In this section we present three examples of the application of m-RSC to derive the counterfactual estimates of possible numberof deaths under the changed conditions like delaying or starting the stringency measures at earlier date. We consider threedifferent units of treatments, namely: The State of New York, Italy and The Indian capital city Delhi. In some sense theseplaces have also been termed as regional epicenters of the epidemic.
State of New York
New York has the highest number of confirmed cases in the United States. First case in New York was reported on 1st March,2020 and New York went into a stricter lock-down on March 22nd, 2020. We estimate counterfactual considering this as dateof intervention. We select among other states from US as donor group using the methods described above. This includes NewJersey, California, Illinois, and Florida among other states. By counterfactual estimate, the number of deaths in New York couldhave been 6 times higher, and number of confirmed cases could have been 5 times higher. eb,2020 Mar,2020 Apr,2020 May,2020 Jun,2020 Jul,2020 − C u m u l a t i v e nu m b e r o f d e a t h s : W H O a nn o un ce s n a m e C O V I D -
19 2/29/20 : U S r e p o r t s fi r s t C O V I D - d e a t h : W H O c l a ss i fi e s C O V I D - a s a p a nd e m i c : N e w Y o r k s c h oo l c l o s u r e : N e w Y o r k l o c k d o w n : N e w Y o r k s a w i t s l a r g e s t s i n g l e - d a y i n c r e a s e i nd e a t h s : N e w Y o r k o u t li n e d fi r s t s t e p s t o w a r d s e a s i n g l o c k d o w n r e s t r i c t i o n s : F a u c i w a r n e d o f s e r i o u s c o n s e qu e n ce s i f go v e r n o r s r e o p e n s t a t eec o n o m i e s p r e m a t u r e l y : T h o u s a nd s g a t h e r e d a c r o ss U S t o p r o t e s tt h e d e a t h o f G e o r g e F l o y d New York: Cumulative number of deaths over time and chainge points
Feb,2020 Mar,2020 Apr,2020 May,2020 Jun,2020
Date C u m u l a t i v e nu m b e r o f d e a t h s : W H O a nn o un ce s n a m e C O V I D -
19 2/29/20 : U S r e p o r t s fi r s t C O V I D - d e a t h : W H O c l a ss i fi e s C O V I D - a s a p a nd e m i c : N e w Y o r k s c h oo l c l o s u r e : N e w Y o r k l o c k d o w n : N e w Y o r k s a w i t s l a r g e s t s i n g l e - d a y i n c r e a s e i nd e a t h s : N e w Y o r k o u t li n e d fi r s t s t e p s t o w a r d s e a s i n g l o c k d o w n r e s t r i c t i o n s : F a u c i w a r n e d o f s e r i o u s c o n s e qu e n ce s i f go v e r n o r s r e o p e n s t a t eec o n o m i e s p r e m a t u r e l y : T h o u s a nd s g a t h e r e d a c r o ss U S t o p r o t e s tt h e d e a t h o f G e o r g e F l o y d New York: Cumulative number of deaths, Actual and Counterfactual
Observations (Cumulative number of deaths)Predictions (Cumulative number of deaths)Feb,2020 Mar,2020 Apr,2020 May,2020 Jun,2020
Date C u m u l a t i v e nu m b e r o f c o n fi r m e d c a s e s : W H O a nn o un ce s n a m e C O V I D -
19 2/29/20 : U S r e p o r t s fi r s t C O V I D - d e a t h : W H O c l a ss i fi e s C O V I D - a s a p a nd e m i c : N e w Y o r k s c h oo l c l o s u r e : N e w Y o r k l o c k d o w n : N e w Y o r k s a w i t s l a r g e s t s i n g l e - d a y i n c r e a s e i nd e a t h s : N e w Y o r k o u t li n e d fi r s t s t e p s t o w a r d s e a s i n g l o c k d o w n r e s t r i c t i o n s : F a u c i w a r n e d o f s e r i o u s c o n s e qu e n ce s i f go v e r n o r s r e o p e n s t a t eec o n o m i e s p r e m a t u r e l y : T h o u s a nd s g a t h e r e d a c r o ss U S t o p r o t e s tt h e d e a t h o f G e o r g e F l o y d New York: Cumulative number of confirmed cases, Actual and Counterfactual
Observations (Cumulative number of confirmed cases)Predictions (Cumulative number of confirmed cases)
Figure 1.
New York State: (a) Actual number of deaths with linear trend line and points where trend changed (b) Actualnumber of deaths with counterfactual prediction estimated by m-RSC with actual lock-down date as intervention point (c)Actual number of confirmed cases with counterfactual prediction estimated by m-RSC. eb,2020 Mar,2020 Apr,2020 May,2020 Jun,2020 Jul,2020 − C u m u l a t i v e nu m b e r o f d e a t h s : W H O a nn o un ce s n a m e C O V I D -
19 2/20/20 : F i r s t r e p o r t e d c a s e i n I t a l y : c o n fi r m e d c a s e s i n L o m b a r d y :I t a l y b ec a m e t h e w o r s t - h i t c o un t r y i n E u r o p e :I t a l y b e g i n s L o c k d o w n : L o c k d o w n e x t e nd e d t o w h o l e I t a l y : W H O c l a ss i fi e s C O V I D - a s a p a nd e m i c : E U t r a v e l r e s t r i c t i o n :I t a l y r ec o r d s m o r ec o r o n a v i r u s - r e l a t e dd e a t h s t h a n C h i n a :I t a l y e x t e nd s l o c k d o w n : L o w e s t nu m b e r o f n e w d a il y c a s e s i n t h r ee w ee k s : E u r o p e r e a c h e d , c o r o n a v i r u s d e a t h s : A r o und m illi o n I t a li a n s r e t u r n e d t o w o r k : R e s t a u r a n t s a nd s h o p s r e o p e n e d i n I t a l y Italy: Cumulative number of deaths over time and chainge points
Feb,2020 Mar,2020 Apr,2020 May,2020 Jun,2020
Date C u m u l a t i v e nu m b e r o f d e a t h s : W H O a nn o un ce s n a m e C O V I D -
19 2/20/20 : F i r s t r e p o r t e d c a s e i n I t a l y : c o n fi r m e d c a s e s i n L o m b a r d y :I t a l y b ec a m e t h e w o r s t - h i t c o un t r y i n E u r o p e :I t a l y b e g i n s L o c k d o w n : L o c k d o w n e x t e nd e d t o w h o l e I t a l y : W H O c l a ss i fi e s C O V I D - a s a p a nd e m i c : E U t r a v e l r e s t r i c t i o n :I t a l y r ec o r d s m o r ec o r o n a v i r u s - r e l a t e dd e a t h s t h a n C h i n a :I t a l y e x t e nd s l o c k d o w n : L o w e s t nu m b e r o f n e w d a il y c a s e s i n t h r ee w ee k s : E u r o p e r e a c h e d , c o r o n a v i r u s d e a t h s : A r o und m illi o n I t a li a n s r e t u r n e d t o w o r k : R e s t a u r a n t s a nd s h o p s r e o p e n e d i n I t a l y Italy: Cumulative number of deaths, Actual and Counterfactual
Observations (Cumulative number of deaths)Predictions (Cumulative number of deaths)Feb,2020 Mar,2020 Apr,2020 May,2020 Jun,2020
Date C u m u l a t i v e nu m b e r o f c o n fi r m e d c a s e s : W H O a nn o un ce s n a m e C O V I D -
19 2/20/20 : F i r s t r e p o r t e d c a s e i n I t a l y : c o n fi r m e d c a s e s i n L o m b a r d y :I t a l y b ec a m e t h e w o r s t - h i t c o un t r y i n E u r o p e :I t a l y b e g i n s L o c k d o w n : L o c k d o w n e x t e nd e d t o w h o l e I t a l y : W H O c l a ss i fi e s C O V I D - a s a p a nd e m i c : E U t r a v e l r e s t r i c t i o n :I t a l y r ec o r d s m o r ec o r o n a v i r u s - r e l a t e dd e a t h s t h a n C h i n a :I t a l y e x t e nd s l o c k d o w n : L o w e s t nu m b e r o f n e w d a il y c a s e s i n t h r ee w ee k s : E u r o p e r e a c h e d , c o r o n a v i r u s d e a t h s : A r o und m illi o n I t a li a n s r e t u r n e d t o w o r k : R e s t a u r a n t s a nd s h o p s r e o p e n e d i n I t a l y Italy: Cumulative number of confirmed cases, Actual and Counterfactual
Observations (Cumulative number of confirmed cases)Predictions (Cumulative number of confirmed cases)
Figure 2.
Italy: (a) Actual number of deaths with linear trend line and points where trend changed (b) Actual number ofdeaths with counterfactual prediction estimated by m-RSC with actual lock-down date as intervention point (c) Actual numberof confirmed cases with counterfactual prediction estimated by m-RSC.
Italy
Italy was put under lock-down between 8th March, 2020 - 4th May, 2020. We considered most European countries to model thedonor group and selected based on criteria defined above. Based on our simulation, we observe that with lock-down measureshas been largely successful in Italy. Without such measures, the number of confirmed case could have been 8 times higher andnumber of deaths could have been 3 times higher by 26th of June, 2020.
Delhi, India
India had one of the most strict stay home order across the country in first phase of the lock-down between 25 March 2020– 14 April 2020 (21 days), where an entire population of 1.3 billion people was put under restricted movement. Overall thelock-down had multiple phases, second phase was from 15th of April 2020 to 3rd of May 2020, and third phase was 4th of Mayto 17th of May, 2020. We present the counterfactual for each of these dates. However, in this case we consider both the dailynumber of confirmed cases as well as the cumulative number of confirmed cases for phase three of the lock-down. We limit thedonor group as all others states of India.Figure 3 shows that counterfactual converges closely with the actual at third phase of the lock-down. It should be noted thatthere are a few discrepancies in reporting. First, there is a weekly seasonality - possibly due to a lesser number of reports overthe weekends. Second due to a revised higher number of reports on certain dates (high peak). ar,2020 Apr,2020 Apr,2020 Apr,2020 May,2020 May,2020 Jun,2020 Jun,2020 Jul,2020 D a il y nu m b e r o f c o n fi r m e d : A c o m p l e t e - d a y n a t i o n a ll o c k d o w n : T h e d o ub li n g r a t e h a d s l o w e d t o s i x d a y s f r o m t h r ee d a y s :I nd i a e x t e nd e d t h e n a t i o n w i d e l o c k d o w n : T h e I nd i a n go v e r n m e n t a ll o w e d a li m i t e d r e o p e n i n g 5/3/20 :I nd i a e x t e nd e d i t s n a t i o n w i d e l o c k d o w n f o r a n o t h e r t w o w ee k s : L o c k d o w n e x t e nd e d t ill J un e i n c o n t a i n m e n t z o n e s Delhi: Daily number of confirmed over time and chainge points
Mar,2020 Apr,2020 Apr,2020 May,2020 May,2020 Jun,2020 Jun,2020
Date D a il y nu m b e r o f c o n fi r m e d c a s e s : A c o m p l e t e - d a y n a t i o n a ll o c k d o w n : T h e d o ub li n g r a t e h a d s l o w e d t o s i x d a y s f r o m t h r ee d a y s :I nd i a e x t e nd e d t h e n a t i o n w i d e l o c k d o w n : T h e I nd i a n go v e r n m e n t a ll o w e d a li m i t e d r e o p e n i n g 5/3/20 :I nd i a e x t e nd e d i t s n a t i o n w i d e l o c k d o w n f o r a n o t h e r t w o w ee k s : L o c k d o w n e x t e nd e d t ill J un e i n c o n t a i n m e n t z o n e s Delhi: Daily number of confirmed cases, Actual and Counterfactual
Observations (Daily number of confirmed cases)Predictions (Daily number of confirmed cases)Mar,2020 Apr,2020 Apr,2020 May,2020 May,2020 Jun,2020 Jun,2020
Date D a il y nu m b e r o f c o n fi r m e d c a s e s : A c o m p l e t e - d a y n a t i o n a ll o c k d o w n : T h e d o ub li n g r a t e h a d s l o w e d t o s i x d a y s f r o m t h r ee d a y s :I nd i a e x t e nd e d t h e n a t i o n w i d e l o c k d o w n : T h e I nd i a n go v e r n m e n t a ll o w e d a li m i t e d r e o p e n i n g 5/3/20 :I nd i a e x t e nd e d i t s n a t i o n w i d e l o c k d o w n f o r a n o t h e r t w o w ee k s : L o c k d o w n e x t e nd e d t ill J un e i n c o n t a i n m e n t z o n e s Delhi: Daily number of confirmed cases, Actual and Counterfactual
Observations (Daily number of confirmed cases)Predictions (Daily number of confirmed cases)Mar,2020 Apr,2020 Apr,2020 May,2020 May,2020 Jun,2020 Jun,2020
Date D a il y nu m b e r o f c o n fi r m e d c a s e s : A c o m p l e t e - d a y n a t i o n a ll o c k d o w n : T h e d o ub li n g r a t e h a d s l o w e d t o s i x d a y s f r o m t h r ee d a y s :I nd i a e x t e nd e d t h e n a t i o n w i d e l o c k d o w n : T h e I nd i a n go v e r n m e n t a ll o w e d a li m i t e d r e o p e n i n g 5/3/20 :I nd i a e x t e nd e d i t s n a t i o n w i d e l o c k d o w n f o r a n o t h e r t w o w ee k s : L o c k d o w n e x t e nd e d t ill J un e i n c o n t a i n m e n t z o n e s Delhi: Daily number of confirmed cases, Actual and Counterfactual
Observations (Daily number of confirmed cases)Predictions (Daily number of confirmed cases)Mar,2020 Apr,2020 Apr,2020 May,2020 May,2020 Jun,2020 Jun,2020
Date C u m u l a t i v e nu m b e r o f c o n fi r m e d c a s e s : A c o m p l e t e - d a y n a t i o n a ll o c k d o w n : T h e d o ub li n g r a t e h a d s l o w e d t o s i x d a y s f r o m t h r ee d a y s :I nd i a e x t e nd e d t h e n a t i o n w i d e l o c k d o w n : T h e I nd i a n go v e r n m e n t a ll o w e d a li m i t e d r e o p e n i n g 5/3/20 :I nd i a e x t e nd e d i t s n a t i o n w i d e l o c k d o w n f o r a n o t h e r t w o w ee k s : L o c k d o w n e x t e nd e d t ill J un e i n c o n t a i n m e n t z o n e s Delhi: Cumulative number of confirmed cases, Actual and Counterfactual
Observations (Cumulative number of confirmed cases)Predictions (Cumulative number of confirmed cases)
Figure 3.
Delhi, India: (a) Actual number of confirmed cases with trend line and points where trend changed (b) Actualnumber of confirmed cases with counterfactual prediction estimated by m-RSC with First lock-down date as intervention point(c) On Second lock-down date (d) On third lock-down date inear trend-line fit shows two change points in the growth of number of cases - indicating that the exponential phase cameat much later date and growth of the epidemic was under effective control in the earlier stages. Since, the stay-home order wasapplicable across all states and adherence was almost uniform - trajectory of actual and counterfactual remains nearly same.
Discussion
In this work we use Multi-dimensional Robust Synthetic Control to understand the effects of stringency measure on COVID-19pandemic. We construct synthetic version of a location using convex combination of other geographic locations in the donorpool that most closely resembled the treatment unit in terms of pre-intervention period using stringency index and adherencescore (using mobility information). Results has been compared for The State of New York, Italy and Delhi, India with actualmetric to that of counterfactual predicted by the algorithm.In order to assess the robustness of the predictor we have computed MAPE and MdAPE measures and have shown theirconvergence to less than 20% absolute error rate. In the future we would like to include additional predictors like testing data,and virus strain information as they become available. Another direction of this study is to include parametric epidemic modelslike SIR-F , and compare with m-RSC. Methods
Tools
As stated above, our objective is to study the effects of government response at an aggregate level in terms of lives saved, andlimiting the number of cases that require hospitalization. Such interventions can effectively be studied at a comparative level.In other words, if we have data for the evolution of aggregate outcomes, e.g. the number of confirmed cases and deaths, whenpolicy is applied in a group under study versus when the same policy is not applied in a control group. However, governmentpolicies were applied at different level across a geographic region. We do not have a mechanism to conduct a randomized trial.Hence, we consider using the synthetic control method . In a synthetic control set up, where observational data is availablefor different groups, we can construct a synthetic or virtual control group by combining measurements from alternatives (ordonors). In the following, we provide a brief overview of m-RSC .Suppose that observations from N different geographically distinct groups or units are indexed by i ∈ [ N ] in T time periods(days) indexed by j ∈ [ T ] . Let k ∈ [ K ] be the metrics of interest (e.g. number of confirmed cases, number of deceased, numberof tests conducted, etc.). By M i jk we denote the ground-truth measurement of interest, and by X i jk , an observation of thismeasurement with some noise. Let 1 ≤ T ≤ T be the time instance in which our group of interest experiences an intervention,namely a government response to control the spread (e.g. stay home order, school or business closure, or mass vaccination).Without loss of generality we consider unit i = k = k = i = ≤ i ≤ N ), and metrics k ∈ [ K ] . In the following we make two assumptions: (1) for all 2 ≤ i ≤ N , k ∈ [ K ] and j ∈ [ T ] , we have X i jk = M i jk + ε i jk where, ε i jk is the observational noise, and (2) Same model is obeyed by i = j ∈ [ T ] and k ∈ [ K ] we have X jk = M jk + ε jk . As described by authors in , in following we also assume that for unit i =
1, we only observe themeasurement X jk for pre-intervention period, i.e. for all j ∈ [ T ] and k ∈ [ K ] . Our objective is to compute a counterfactualsequence of observation M jk for the time period j ∈ [ T ] , and k ∈ [ K ] , and in specific for T ≤ j ≤ T , and k =
1, using syntheticversion of unit i = M = [ M i jk ] ∈ R N × T × K . M is assumed to have a few well behaved properties as required by the algorithm, namely,(1) M must be approximately low-rank and (2) every element (cid:12)(cid:12) M i jk (cid:12)(cid:12) shall have boundedness property (for details see ). Tocheck whether our model assumption holds in practice, we consider N = , T = , K =
2, with 185 countries as units. Weconsider number of confirmed cases and number of deceased as two metrics over 150 days between January 22, 2020 and June20, 2020. For assumption to hold, data matrix corresponding to number of confirmed cases and number of deceased and theircombination should be approximated by a low-rank matrix.As shown in Figure 4, the spectrum of the top 20 singular values (sorted in descending order) for each matrix. The plotsclearly support the implications that most of the spectrum is concentrated within the top 5 principal components. The sameconclusion holds true when units are states of The United States, and when we consider only countries in The European Union.Let Z ∈ R ( N − ) × T × K corresponding to donor units, and X ∈ R × T × K correspond to unit under intervention. We obtainˆ M from Z after applying a hard singular value thresholding. Subsequently, weights are learned using linear regression bycomputing igure 4. The Singular Value spectrum for all countries (of dimensions 185 × β = arg min v ∈ R ( N − ) (cid:13)(cid:13) X − v T ˆ M T (cid:13)(cid:13) For every k ∈ [ K ] , the corresponding estimated counterfactual means for the treatment unit is then defined asˆ M ( k ) = ˆ β T ˆ M ( k ) Measures of stringency and mobility
As described in Section , we use m-RSC to construct a synthetic control for the treatment unit using data from multiple controlunits or donor group using pre-intervention period data. The synthetic control is then used for estimating the counterfactualin the post-intervention period. In our setup, intervention date is typically the date when a stay-home order or lock-downwas declared for the treatment unit. However, government policy may have been applied over time with different levels ofstringency measures.To understand this we use stringency and policy indices data from OxCGRT , which records the strictness of policies thatrestrict people’s behavior and includes 8 different measures - e.g. school and workplace closure, cancellation of public events,restrictions on gathering size etc. Figure 5, shows the plot of stringency index, with mobility data.It can be observed that the level of lock-down varies over time and geographic region. We use this information in twodifferent ways. First we choose the maximum level of index, first increased level of restriction index, and 14 days after themaximum level of index as various intervention dates and compare their effects. Second, we combine this information withmobility data to select the control groups for a treatment unit as discussed below.In order to understand the effect of stringency on a treatment unit for a metric, we need to select a donor group where levelof stringency was different or adherence to stringency was different. Since, there was a degree of stringency and adherence tosuch measures at different level - under any possible choice of donor group, we acknowledge, that we will be underestimatingthe counterfactual - i.e. what would have been without any stringency measures. To estimate the degree of adherence tolock-down measures, we use mobility data from Apple, Google and Facebook. Apple mobility data provides a relative volumeof directions requests per region, sub-region or city compared to a baseline volume - i.e. percentage change over time from the % C hnage f r o m ba s e li ne Government Response Stringency Index and Mobility Trends in Italy
WalkingDrivingPublic TransportStaying putRelative change in movementGovernment Response Stringency Index ((0 to 100, 100 = strictest))03-01 03-15 04-01 04-15 05-01 05-15 06-01 06-151007550250255075100 % C hnage f r o m ba s e li ne Government Response Stringency Index and Mobility Trends in Germany
WalkingDrivingPublic TransportStaying putRelative change in movementGovernment Response Stringency Index ((0 to 100, 100 = strictest))03-01 03-15 04-01 04-15 05-01 05-15 06-011007550250255075100 % C hnage f r o m ba s e li ne Government Response Stringency Index and Mobility Trends in Sweden
WalkingDrivingPublic TransportStaying putRelative change in movementGovernment Response Stringency Index ((0 to 100, 100 = strictest))
Figure 5.
Stringency index, and Mobility Trends in (a) Italy (b) Germany (c) Swedenbaseline including weekly seasonality. Facebook data provides the relative percentage of population that is staying in the sameplace and also the percentage of population that moved from a region to another. In Facebook data, to quantify how muchpeople move around measure is derived by counting the number of level-16 Bing tiles (which are approximately 600 metersby 600 meters in area at the equator) they are seen in within a day. Assuming U d , r is the set of eligible users in region r onday d , and tiles ( u ) is the number of tiles visited by a given user u in U d , r , total number of tiles visited for that region is givenby totaltiles ( U d , r ) = ∑ u ∈ U d , r min ( tiles ( u ) , ) . Change in Movement measure is then the difference between a baseline andvalue on day d for average number of totaltiles ( U d , r ) . Similarly, Stay Put metric is calculated as the percentage of eligiblepeople who are only observed in a single level-16 Bing tile during the course of a day on an average compared to a baseline.Finally, Google Community Mobility Report provides a percent change in visits to places like grocery stores and parks within ageographic area from baseline.It can be seen from Figure 5, that the adherence and stringency level do not correspond. For example, in Sweden, withincreasing level of government measures between March - April, there has not been any significant change in proportion ofpeople staying put or moving between regions. Similarly, in other places, it can be observed that while government measuresremain at the same level over April, number of people staying put at one place starts declining.Selecting donor group: We combine metrics that allow the spread of the virus and similarly combine those that reduces thepossibility of spread. We combine them by taking average define a single adherence score. For unit i ∈ [ N ] , ∀ j (cid:54) = i : j ∈ [ N ] , j isa donor unit if adherence score, and stringency Index of j is less than i . Figure 6 shows this relation in graphical form for aselected set of countries. As per Figure 6, United States, Brazil and United Kingdom are in the donor group when we computecounterfactual estimate for Italy.Statistical Performance Evaluation: in Figure 7 we present the distribution of Mean and Median absolute percentage errorstatistic for the runs-forecasts from m-RSC algorithm with changing forecast horizon. We consider every Mondays betweenMarch 1, 2020 to June 21, 2020, both included to forecast the number of deaths at the end of the day on June 26, 2020 forall states in United States, and compare with actual data. For every state, donor group is selected using the method describedabove. It can be seen from Figure 7, that both Mean and Median absolute percentage error statistic are larger, when largerforecast horizon has been considered, and that is to be expected. Both MAPE and MdAPE converge to a less than 20 percentwhen horizon is about a week. MAPE being very large from MdAPE clearly indicates a right skew in the predicted values. Adherence Score M ean S t r i ngen cy I nde x It a l y S p a i n F r a n c e G e r m a n y S w e d e n U n i t e d K i n g d o m B e l g i u m N e t h e r l a n d s U n i t e d S t a t e s A u s t r a li a D e n m a r kJ a p a n B r a z il P h ili p p i n e s N e w Z e a l a n d
30 40 50 60 70 80 90
Adherence Score M ean S t r i ngen cy I nde x It a l y S p a i n F r a n c e G e r m a n y S w e d e n U n i t e d K i n g d o m B e l g i u m N e t h e r l a n d s U n i t e d S t a t e s A u s t r a li a D e n m a r kJ a p a n B r a z il P h ili p p i n e s N e w Z e a l a n d Figure 6.
Adherence score vs. Stringency index where size of each circle is determined by (a) total number of deaths till date(b) total number of confirmed cases till date.
Intervention Dates
APE forecast error for US data
MAPE ScoreMdAPE Score
Figure 7.
MAPE ata source Description
Daily update from JHU We use this data to derive metric for units: i.e. number of confirmedcases and number of deceased for each day and geographic locations.Facebook Movement Range Maps The relative percentage of population that is staying put and also thepercentage of population that moved from a region to another. We usethis data in selection of donor units.Apple Mobility Trends Relative volume of directions requests per region, sub-region or citycompared to a baseline volume, categorized by Driving, Walking orPublic Transport. We use this data in selection of donor units.OxCGRT Strictness of policies that restrict people’s behavior, 8 measures com-bined to provide a score between 0 and 100, where 100 being moststringent. We use this data in selection of donor units.Google Community Mobility Re-port Percent change in visits to places like grocery stores and parks withina geographic area. We use this data in selection of donor units.
Table 1.
Data SourceThis exactly corresponds to the places where exponential growth of the pandemic can be observed by March 22, 2020. Thecounterfactual prediction for June 26, 2020 on March 22, 2020 for these few places are several times higher as as expected,while, stricter stringency measures were being implemented in The United States around those dates.
Data Source
We use following five sources of data as described in Table 1:
Authors’ contributions
S. K. G.: Conceptualization, Data Collection, Software, Visualization, Writing - Original Draft, Writing - Review and Editing.S. G.: Writing - Original Draft, Writing - Review and Editing. S. S. N.: Data collection, Writing - Review and Editing. Allauthors reviewed the manuscript.
Data and Code
All data and code used for this work is made available here: https://github.com/subhaskghosh/lockdown-paper
Competing Interests statement
The authors have no competing interests.
References Y. Liu, A. A. Gayle, A. Wilder-Smith, J. Rocklöv, The reproductive number of covid-19 is higher compared to sarscoronavirus, Journal of Travel Medicine 27 (2). doi:10.1093/jtm/taaa021 .URL https://doi.org/10.1093/jtm/taaa021 G. Viceconte, N. Petrosillo, Covid-19 r0: Magic number or conundrum?, Infectious disease reports 12 (1) (2020) 8516–8516.URL https://pubmed.ncbi.nlm.nih.gov/32201554 A. Banerjee, L. Pasea, S. Harris, A. Gonzalez-Izquierdo, A. Torralbo, L. Shallcross, M. Noursadeghi, D. Pillay, N. Sebire,C. Holmes, C. Pagel, W. K. Wong, C. Langenberg, B. Williams, S. Denaxas, H. Hemingway, Estimating excess 1-yearmortality associated with the covid-19 pandemic according to underlying conditions and age: a population-based cohortstudy, The Lancet 395 (10238) (2020) 1715–1725. A. Rismanbaf, Potential treatments for covid-19; a narrative literature review, Archives of academic emergency medicine8 (1) (2020) e29–e29. . S. Price, S. Singh, S. Ledot, P. Bianchi, M. Hind, G. Tavazzi, P. Vranckx, Respiratory management in severe acuterespiratory syndrome coronavirus 2 infection, European Heart Journal: Acute Cardiovascular Care 9 (3) (2020) 229–238. doi:10.1177/2048872620924613 .URL https://doi.org/10.1177/2048872620924613 A. Abadie, A. Diamond, J. Hainmueller, Synthetic control methods for comparative case studies: Estimating the effectof california’s tobacco control program, Journal of the American Statistical Association 105 (490) (2010) 493–505. doi:10.1198/jasa.2009.ap08746 . M. Amjad, D. Shah, D. Shen, Robust synthetic control, Journal of Machine Learning Research 19 (22) (2018) 1–51. M. Amjad, V. Misra, D. Shah, D. Shen, Mrsc: Multi-dimensional robust synthetic control, Proc. ACM Meas. Anal. Comput.Syst. 3 (2). doi:10.1145/3341617.3326152 .URL https://doi.org/10.1145/3341617.3326152 W. C. Koh, L. Naing, J. Wong, Estimating the impact of physical distancing measures in containing covid-19: an empiricalanalysis, medRxiv doi:10.1101/2020.06.11.20128074 . E. Kong, D. Prinz, The impact of shutdown policies on unemployment during a pandemic 24–72 arXiv:https://cepr.org/sites/default/files/news/CovidEconomics17.pdf . M. Supino, A. d’Onofrio, F. Luongo, G. Occhipinti, A. Dal Co, The effects of containment measures in the italian outbreakof covid-19, medRxiv doi:10.1101/2020.03.25.20042713 . D. Ibarra-Vega, Lockdown, one, two, none, or smart. modeling containing covid-19 infection. a conceptual model,Science of The Total Environment 730 (2020) 138917. doi:https://doi.org/10.1016/j.scitotenv.2020.138917 . M. Chinazzi, J. T. Davis, M. Ajelli, C. Gioannini, M. Litvinova, S. Merler, A. Pastore y Piontti, K. Mu, L. Rossi, K. Sun,C. Viboud, X. Xiong, H. Yu, M. E. Halloran, I. M. Longini, A. Vespignani, The effect of travel restrictions on the spread ofthe 2019 novel coronavirus (covid-19) outbreak, Science 368 (6489) (2020) 395–400. arXiv:https://science.sciencemag.org/content/368/6489/395.full.pdf , doi:10.1126/science.aba9757 .URL https://science.sciencemag.org/content/368/6489/395 T. Hale, S. Webster, A. Petherick, T. Phillips, B. Kira, Variation in government responses to covid-19.URL
E. Dong, H. Du, L. Gardner, An interactive web-based dashboard to track COVID-19 in real time, Lancet Infect Dis 20 (5)(2020) 533–534.
K. Jin, L. McGorman, Data for good: New tools to help health researchers track and combat COVID-19 (4 2020).URL https://about.fb.com/news/2020/04/data-for-good/
Apple, Mobility trends reports.URL
J. Fitzpatrick, K. DeSalvo, Helping public health officials combat covid-19.
C. I. Siettos, L. Russo, Mathematical modeling of infectious disease dynamics, Virulence 4 (4) (2013) 295–306,23552814[pmid]. doi:10.4161/viru.24041 .URL https://pubmed.ncbi.nlm.nih.gov/23552814https://pubmed.ncbi.nlm.nih.gov/23552814