# Covid-19: Is it possible to get to r0 < 1 through social distancing measures?

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I'm trying to wrap my head around some of the information I'm reading about how to fight Covid-19 and conflicting opinions about how much "social distancing" is required to avert a disaster, or whether social distancing works at all. (I am a data scientist, not a biologist or medical professional)

First I want to check if some of my assumptions are correct or not:

1. Flattening the curve doesn't reduce the overall number of infections, only the average rate of infection for a given time period, e.g. Flattening the curve doesn't take you from 1000 infected people to 100 infected people, it takes you from 1000 infected people in a week to 1000 infected people in 3 months (numbers are just examples): True or False?
2. The purpose of social distancing is to flatten the curve, not to reduce the number of overall cases: True or False?
3. If $$r_0 > 1$$ than growth is exponential: True or false?
4. Sub-exponential growth can only happen if $$r_0 leq 1$$: True or false?
5. Flattening the curve cannot reduce exponential growth in number of cases to sub exponential growth, it only leads from steep exponential growth, e.g. $$r_0 approx 2.5$$ or $$r_0 approx 3$$, to "not so steep" exponential growth $$r_0 approx 1.5$$ or $$r_0 approx 1.2$$: True or False?

Assuming 1-5 are correct, here are the more complex questions I am trying to figure out:

• Can social distancing (without hard quarantines, tracking as many cases as possible, and instantly isolating any new cases discovered, etc… ) actually lead to $$r_0 < 1$$ and therefore reduce the number of infections as opposed to just spreading them out to a manageable rate?

• I think the answer is "No", because of small world network theory: The majority of people respect prefect social distancing, i.e. they maintain zero social contact with anybody outside of their immediate family and the the people they interact with for procuring life essentials. Because the number of people who cannot practice social distancing due to their essential role in society (grocery and pharmacy employees, health care professionals, law enforcement, etc… ) will still experience very high transmission rates, a small world phenomenon occurs, where the average chain of transmission is still very short between any two individuals in an impacted area. What is wrong with this line of reasoning?

• In general, is $$r_0 < 1$$ achievable without a cure, a vaccine, herd immunity, or the ability to track infections with very high accuracy and isolating them instantly?

I believe r0 is an exponent…

It is the average number of individuals who become infected by each infected individual.

If one infected individual infects exactly one other individual (r0 = 1), the progress will be straight line; the rate will be a flat line based on "mean time between infections"; total number of infections over time will be linear sloping upwards.

If r0 > 1, then it will be an exponential increase; how rapidly/steeply it curves up depends again on the mean time over which that propagation of infection occurs.

If r0 < 1, then it will be an exponential decay. New infections continue to occur, but the overall rate of infection decreases toward but never quite reaching zero.

## Socializing in the time of COVID

Credit: Pixabay/CC0 Public Domain

If working practices and education have been compromised by the ongoing COVID-19 pandemic, then so too, obviously, have our social lives. The limitations of lockdowns and keeping apart to reduce the risk of catching or passing on the virus have been at the forefront of our minds for many months now. The usual places we might gather such as pubs and restaurants, theaters and festivals have all been off-limits periodically in many parts of the world in response to the disease.

How might we stick together even while we are apart? Ardion Beldad of University College Twente in Enschede, The Netherlands, discusses a possible answer to that question looking at how we might sustain our "social capital" through our online activity and the web-based communities in which we dwell, virtually speaking.

As a social animal, the concept of social distancing is very much at odds with our inherent nature. Of course, over the last few years before the COVID-19 pandemic, many people had adopted online technologies for many aspects of their lives. The difference now is that many are essentially obliged to now adopt an online-only social life because of the risk of infection. Unfortunately, the digital divide can now be seen as a gaping maw given that there are many less privileged in society who simply do not have the economic means to access the internet from home, for instance. How we might address this problem is discussed in Beldad's paper.

Beldad also looks at the implications for privacy of the increasingly widespread adoption of online socializing for those who do have access as well as the potential implications for mental health of spending increasing amounts of time in a virtual world, rather than the physical world.

It is worth noting that at the time of writing this article, more or less effective vaccines are now in place in various parts of the world, but much work remains to be done in terms of vaccinating a sufficiently large proportion of the world population to allow us to overcome this pandemic. There are also the ongoing issues of the inevitable emergence of genetic variants of the original virus, which may well have a different susceptibility to the original vaccines.

"The clamor to return to normal face-to-face interactions is expectedly intensifying after months of social distancing measures, Beldad writes. "But until an effective vaccine for COVID-19 is developed, people are left with no other choice but to maintain their connections and interactions online."

## Modeling study suggests 18 months of COVID-19 social distancing, much disruption

On Mar 16, when White House coronavirus response coordinator Deborah Birx, MD, stood beside President Donald Trump and announced the "15 Days to Slow the Spread" campaign, she said guidance on home isolation was informed by the latest models from the United Kingdom.

Birx was likely referring to a new modeling study on likely US and UK outcomes during the COVID-19 pandemic, published yesterday by a team of epidemiologists at the Imperial College of London.

The study, which used pandemic data gathered in China, Italy, and South Korea, has been lauded by epidemiologists around the world as the most comprehensive prediction of what the US could be facing in the coming months. But it also paints some bleak pictures, including millions of deaths if little is done.

### Flattening the curve vs suppression

The model analyzes the two approaches to managing the virus. One is mitigation, or "flattening the curve," which sees the novel coronavirus continue to spread, but at a slow rate so as not to overwhelm hospital systems. The other approach is suppression, which tries to reverse the pandemic through extreme social distancing measures and home quarantines of cases and their families, achieving an R0—or reproduction number—of less than 1.

"Each policy has major challenges," the authors wrote. Mitigation "might reduce peak healthcare demand by 2/3 and deaths by half. However, the resulting mitigated epidemic would still likely result in hundreds of thousands of deaths and health systems (most notably intensive care units) being overwhelmed many times over."

To avoid that, the country would need to focus on suppression. But suppression requires social distancing measures far longer than the 14 to 30 days Americans have been told to prepare for. Instead, they would need to be in place for 18 months, or until a vaccine is made available.

"I think the model's broad conclusion is correct that there is a terrible dilemma of very long-term social distancing, or overloading healthcare systems, or both," said Marc Lipsitch, DPhil, a professor of epidemiology and the director of the Center for Communicable Disease Dynamics at Harvard University. "With the options currently available I do not see a way to get out of this dilemma."

### Model considers 3 scenarios, predicts high death count

To understand how mitigation or suppression would play out, the Imperial College team, led by Neil Ferguson, OBE, ran a model based on three scenarios. In the first, US officials do nothing to mitigate the spread of COVID-19, schools and businesses are kept open, and the virus is allowed to move through the population.

This would result in 81% of the US population, about 264 million people, contracting the disease. Of those, 2.2 million would die, including 4% to 8% of Americans over age 70. More important, by the second week in April, the demand for critical care beds would be 30 times greater than supply.

If mitigation practices are put in place, including a combination of case isolation, home quarantine, and social distancing of those most at risk (over age 70), the peak critical care demand would reduce by 60%, and there would be half the number of deaths. But this scenario still produces an eightfold demand on critical care beds above surge capacity.

In order to suppress the pandemic to an R0 of below 1, a country would need to combine case isolation, social distancing of the entire population, and either household quarantine or school and university closure, the authors found. These measures "are assumed to be in place for a 5-month duration," they wrote.

In addition, the authors said, these measures may have to be put back into place if restrictions are lifted and cases surge again.

"I don't think it is attractive, [I] just don't see a way out of it," said Lipsitch.

### Americans finally accepting reality, expert says

Maciej Boni, PhD, of the Center for Infectious Disease Dynamics at Pennsylvania State University, said the Imperial College model is the most likely scenario produced on the current pandemic.

"This has been trickling out to the public since [the] last week of February," Boni told CIDRAP News. "Now the public is ready to hear that 1 to 2 million people could die, which is what we [epidemiologists] have said for 3 weeks."

The Imperial College model does not take into account finding or creating a successful antiviral to combat the virus. Boni said that likely reflects the history of antivirals.

"We're not as successful at finding antivirals as antibiotics or antimalarials," he said. "I'm not holding up hope for antivirals."

Boni said the American public should expect a challenging 18 months, noting the country hasn't faced a pandemic of this scale in 102 years, and has enjoyed mostly peace and growth in the last 75 years.

## Coronavirus Social Distancing May Be Reducing Infrasound - What’s That?

The dramatic reductions in human activity because of COVID-19 coronavirus restrictions can be traced to all types of changes. NASA has documented reductions in air pollution, and an article in Nature reports that seismic noise, humming in the Earth’s crust, has decreased. When I posted that article on my public Facebook page, my colleague John Trostel shared another interesting observation being detected at the Georgia Tech Research Institute (GTRI). He wrote, “I'm seeing a reduction in infrasound (sounds below human hearing.. less than 20Hz) also.” Trostel, a principal research scientist at GTRI, says measurements are taken at their facility in metropolitan Atlanta. What is infrasound, and why is it being reduced by less human activity?

PASADENA, CA - MARCH 30: Aerial view of light traffic at the interchange of the 210, 134 and 110 . [+] freeways on March 30, 2020 in Pasadena, California. City officials have implored Southern Californians to practice social distancing and stay to home as much as possible. Pasadena's Rose Bowl area, which is used by soccer teams, runners, walkers and cyclists, was shut down by police yesterday to break up crowds that could spread the virus that causes COVID-19. Health experts warn that the coronavirus (COVID-19) pandemic could come to its first peak in this region in April. (Photo by David McNew/Getty Images)

Before we dig deeper, let’s define infrasound. According to the National Oceanic and Atmospheric Administration (NOAA), infrasound is “sound below the range of human hearing.”

Infrasonics is the study of sound below the range of human hearing. These low-frequency sounds are produced by a variety of geophysical processes including earthquakes, severe weather, volcanic activity, geomagnetic activity, ocean waves, avalanches, turbulence aloft, and meteors and by some man-made sources such as aircraft and explosions. Infrasonic and near-infrasonic sound may provide advanced warning and monitoring of these extreme events.

NOAA ESRL website

In a paper published in Progress in Biophysics and Molecular Biology, Geoff Leventhall discusses facts and myths surrounding infrasound. Infrasound illnesses linked to wind turbines have been debated, but the scholarly “jury” is still out. A 2014 study in the journal Natural Hazards argued that infrasound associated with wind turbines, air movement in ducts, and heavy machinery are correlated with reports of fatigue, malaise, nausea, sleep disruption, and pain. Correlation is not causation, but I was surprised at how many studies are in the literature on the topic.

The picture above shows a normally-busy interchange in California and is a dramatic example of how social distancing restrictions have reduced human activity. President Donald Trump and other leaders have extended many of these measures through the Spring so traffic, industrial, and heavy machinery activities will continue to be limited. The unfortunate crisis has enabled scientific research opportunities similar to what happened when airplanes were grounded after 9/11. Researchers were able to evaluate how condensation trails (contrails) from aircraft (or the lack thereof) affected the radiation budget of the atmosphere.

### 5 Things To Know About Record-Shattering Heat In The Northwest U.S.

Infrasound measured on March 2nd, 2020. The time is GMT (so offset by 4 hours). The bright bands in . [+] the March 2nd data are when the a nearby wind tunnel was running. The x-axis is time of day from 00 to 24 Greenwich Mean Time. The y-axis is frequency (of the acoustic energy) from 0 to 25 Hz. Audible sound is generally considered to be above 20 Hz. The colors indicate the amount of energy at each frequency. The wind tunnel is broad band acoustic energy with a big peak at about 23 Hz.

Same data as previous graphic but on March 31st, 2020

John Trostel believes that the coronavirus “shutdown” is presenting a similar opportunity with infrasound. He shared spectrogram plots from March 2nd (at the beginning of the COVID-19 crisis) and March 31st, when significant social distancing measures and policies had been established around the nation. The bright bands in the March 2nd data (top graphic) are when a nearby wind tunnel was running and is likely a manifestation of infrasound detection. There are no corresponding bands in the data from March 31st (bottom graphic).

The wind tunnel is broad band acoustic energy with a big peak at about 23 Hz. The plot from March 31st does not have these bands. There are many sources of infrasound produced by us now days. There is traffic noise, trains, airplanes and helicopters, AC units etc. The Severe Storms Research Center at GTRI is trying to use infrasound (below 20 Hz) to detect and track severe storms at a distance using an array of sensors at our facility in Cobb County. This may be important to detect storms in areas far from NEXRAD radars or those storms that are low-topped and therefore hard to detect by radar.

John Trostel, GTRI

Trostel reminded me that the noise produced by other sources tends to mask the infrasound from storms and other natural sources. The absence of the human produced infrasound may allow us to detect weather phenomena better with "urban arrays” like the one GTRI is evaluating. Trostel believes more infrasound signal may be detectable in the coming weeks as less background noise is present because of reductions in anthropogenic (human-related) activities.

## Loosening COVID-19 Social Distancing Interventions: Lessons Learned from Abroad

As of the end of April 2020, there are more than 3 million confirmed cases of COVID-19 resulting in over 200,000 deaths across approximately 200 countries. While initial containment efforts to identify and isolate cases as well as trace and quarantine close contacts have been attempted to varying degrees of success across the world, virtually every country has found it necessary to also implement community mitigation strategies to slow the spread of the pandemic.

In the United States these strategies, which include personal protective measures, have been previously recommended and utilized to respond to pandemic influenza. For example, school closures, social distancing in workplaces, and postponing or cancelling mass gatherings are thought to slow the acceleration in the number of cases, reduce the peak number of cases and related demands on hospitals and infrastructure, and decrease the number of overall cases and health effects. This is, in essence, what “flattening” the pandemic curve is attempting to do.

In response to COVID-19, most states have implemented these specific strategies in addition to broader ones, including stay-at-home orders and closures of nonessential businesses. On April 13, the Centers for Disease Control and Prevention published preliminary evidence from four metropolitan areas across the country showing that using a combination of these strategies reduces community mobility – a proxy measure for social distancing – and are likely contributing to slowing the spread of infections.

Over the last several weeks, it appears the United States reached a plateau of approximately 30,000 new confirmed cases and 2,000 deaths daily. One caveat with confirmed cases is that testing unfortunately plateaued as well thus, the percentage of positive COVID-19 tests may be a better indicator to gauge whether testing is sufficiently widespread to provide good data on which policymakers can act. Using that variable, it appears half of the states may not yet be past their peak.

Nevertheless, given the significant adverse economic consequences of community mitigation measures, there has been growing pressure to gradually begin lifting social distancing interventions. On April 16, President Trump unveiled the administration’s Guidelines for Opening Up America Again to assist states and localities in reopening their economies while still protecting American lives. Some states have followed suit and taken steps to ease restrictions and have offered detailed plans to do so over the coming weeks and months. Various organizations have also shared important guidance documents to support governors in this regard. There is general consensus that a more robust testing infrastructure which promptly leads to the identification and isolation of cases, a public health system that is well funded and supported to lead contact tracing efforts, and a health care system with capacity and available personal protective equipment and critical medical material are essential to successfully loosening community mitigation measures.

One additional input that could be important to decision-makers involves analyzing the response of various countries around the world that are temporally similar to or ahead of the United States on their respective pandemic curves and are either contemplating or already in the process of loosening social distancing interventions. Researchers have started tracking and comparing the quantity and strictness of containment efforts and community mitigation strategies across various countries over time through a Stringency Index. Continued tracking as the initial pandemic wave recedes will help to assess how countries are loosening government policies. East Asian countries such as China and South Korea are the furthest along in opening up their business sectors, while countries such as Hong Kong and Singapore still have significant restrictions in place after a March spike in infections. Many European Union countries are also in the process of making decisions with respect to loosening social distancing interventions. Table 1 provides a high-level snapshot as of April 28, 2020 of the impact of COVID-19 on various East Asian and European Union countries.

### Table 1

JurisdictionDeaths/1M popTot Cases/1M popTests/1M popDeaths/Tot Cases
Austria611,69625,1893.6%
Czech Republic2169520,4013.0%
Denmark741,50226,9004.9%
France3572,5417,10314.0%
Germany731,89524,7384.0%
Italy4463,29829,60013.5%
Netherlands2642,23211,31911.8%
Spain5034,90728,77910.3%
Switzerland1923,37028,3435.7%
UK3112,31510,60513.4%
South Korea521011,8692.4%
Taiwan0.3182,5901.7%
China358Unreported5.2%
Singapore22,46520,8150.1%
Hong Kong0.513819,4260.4%

While many of these countries are distinct from the United States with respect to their size, form of government, culture, and extent of personal freedoms, lessons from their experiences could be helpful for U.S. policymakers.

To that end, the Bipartisan Policy Center initiated a study to assess how countries around the world are attempting to relax social distancing interventions as they transition from the initial pandemic wave. To assist with this project, BPC analyzed real-time qualitative data from the Health System Response Monitor – a collaboration of the World Health Organization Regional Office for Europe, the European Commission, and the European Observatory on Health Systems and Policies. BPC also corresponded with experts connected to the Commonwealth Fund’s International Health Policy and Practice Innovations program, reviewed various media reports and published literature, and drew on the expertise of an advisory group (see acknowledgments) which met virtually on April 23, 2020. Focus countries included Austria, the Czech Republic, Denmark, France, Germany, Italy, Netherlands, Spain, Switzerland, the United Kingdom, South Korea, Taiwan, China, Singapore, and Hong Kong.

This white paper includes a case study of Germany’s response and approach to loosening social distancing interventions, preliminary insights from a cross-country analysis, as well as implications and initial recommendations for the United States with respect to loosening social distancing interventions.

### Germany Case Study

Global responses to COVID-19 vary greatly depending on a variety of factors including size, geography, and government structure. There is no one-size-fits-all response as needs and feasibility differ from country to country. In order to take lessons learned from countries that may be temporally ahead of the United States, it is key that these approaches be feasible politically, socially, and economically in our country.

Germany is comparable to the United States in many ways. Importantly, both Germany and the United States have federal systems of government – meaning power is shared between states and the federal government. As such, we highlight Germany’s COVID-19 response and plans to loosen social distancing measures in order to explore best practices to be considered for adoption in the United States.

Response efforts

Germany has the 6th highest number of confirmed cases with more than 160,000 cases and 6,215 deaths. The country saw its first case on January 27. Since then, the German federal and state governments have taken many steps to slow the spread of the virus. Germany’s public health response to COVID-19 can be characterized in five essential areas: health communication, physical distancing, isolation and quarantine, monitoring and surveillance, and testing. Targeted efforts in these areas have led to decreased spread and the ability to reopen the country.

Health communication has been vital in preventing the spread of COVID-19 as these efforts require collective participation. In early February, the German federal government released official recommendations for prevention strategies including hand hygiene, physical distancing when sneezing and coughing, and respiratory etiquette. The federal government leveraged social media to disseminate tutorials for these safety measures. The Robert Koch Institute, or RKI, the government’s central scientific institution in the field of communicable disease, also held daily press briefings to communicate information on the outbreak.

Another critical prevention measure involves physical distancing since person-to-person spread is the primary form of transmission. Though states can have individual plans, German states and the German Chancellor agreed upon similar measures to delay the spread and alleviate the burden on the health care system. Throughout March, federal and state governments gradually implemented more intense physical distancing policies. By March 16, the head of all states decided to close bars, clubs, theaters, and other social spaces. On March 22, all states implemented more social distancing measures including people maintaining 1.5 meters of physical distancing and a ban on more than two-person gatherings. One state, Bavaria, enforced a curfew. The new social distancing measures were set to end in early April but were extended until April 19. Many states announced fines for those who violate social distancing regulations. In addition to physical distancing policies, the country requires isolation and quarantine for confirmed COVID-19 cases and contact persons.

Monitoring and surveillance measures allowed medical officials to track the outbreak. Germany’s RKI regularly updates laboratory testing criteria to ensure those who are most at risk receive testing priority. The criteria for testing have changed throughout the course of the pandemic. In order to determine testing needs, RKI conducted a nationwide laboratory survey. The country has a high capacity for testing with the ability to administer more than 600,000 tests per week. On April 9, RKI announced an antibody study to monitor virus more efficiently where nearly 5,000 tests will be administered per day. Additional antibody studies are in process to sample individuals in four outbreak areas and a broader study looking at a representative sample of 15,000 individuals across 150 locations in Germany.

The Minister of Health also confirmed Germany’s Public Health Service will be deploying team members and utilizing technology to enhance monitoring efforts starting on March 25. All states agreed to have at least one contract tracing team of five public health personnel per 20,000 inhabitants. To support these efforts, public employees from other agencies will provide administrative assistance in identifying and containing COVID-19 outbreaks. If further support is needed in areas of high infection, soldiers and armed forces officials can be utilized. Additionally, the Ministry of Health is providing resources to upgrade reporting software and hardware. These upgrades will help relieve administrative burden on local health offices as symptoms are currently being monitored through daily house calls. Additionally, a German research institute is developing a federally funded COVID-19 app. Users can receive direct notifications from local health authorities on COVID-19 test results and access contract tracing capabilities.

Germany’s Plans to Reopen

Given that there is no vaccine or standard treatment for COVID-19, countries will likely have to adopt a “suppress and lift” strategy. The German government is set to announce official next steps on May 6. However, states generally have the authority to conduct reopening autonomously. As of April 15, German states agreed to gradually lift some social distancing rules including allowing car dealerships, bicycle shops, bookstores, and stores up to 800 square meters to open.

All physical distancing measures will stay in place until May 3 and large gatherings are banned until August 31. In order to decrease transmission while loosening social distancing measures, all federal states have required face masks be worn on public transportation and in stores.

The step-by-step plan is largely contingent upon the virus’ reproduction number and the number of newly infected people per day. These data are dependent on the country’s testing capacity – both for acute infections and past infections. In fact, Germany only considered reopening once its reproduction rate fell below 1, to 0.7 on April 16. Scientists suggest a reproduction rate below 1 means the virus will spread slowly and eventually die out. Testing capacity will serve as a critical public health indicator as these measures can determine the country’s ability to deliver necessary care and contain the virus. According to the World Health Organization, countries with extensive testing have less than 10% of their tests come back positive. Germany is well below that benchmark with a positive result rate of 7.5%.

Areas and population groups with relatively low risk of infection are set to open first. On May 4, schools will begin to reopen. Students leaving secondary school or vocational school this year or have qualification examinations will return on May 4. Students in their final year of primary school will also resume classes on May 4, but younger elementary students do not have a return date set. Prior to any students returning to school, the Standing Conference of Ministries of Education and Cultural Affairs of the Länder in the Federal Republic of Germany must develop a plan for teaching with hygiene, social distancing measures such as such as reduced class sizes, and organization steps to prevent lines or groups from forming.

Bavaria has decided to delay secondary and primary school openings until May 11. Regardless of the reopening date, all schools must adhere to special hygiene standards. Hair and grooming service providers are also allowed to begin reopening with strict hygiene rules.

Due to necessary prevention strategies, economies across the world are suffering. The German government has allocated \$825 billion to support the economy. In addition, German officials have detailed a variety of measures to help the economy and labor market. Economic aid is focused in three areas: extending safety net protections, boosting employment and retention of staff in key sectors, and providing tax relief and direct subsidies. Key to extending social support is expanding childcare to mitigate necessary school and day-care closures. Under the Infection Protection Act, parents who now provide childcare for children up to 12 years of age are eligible to claim compensation for up to 67% of the net income. In order to support small business, the federal government is distributing a one-time emergency supplement depending on the size of the business.

The Ifo Institute for Economic Research recommends priority for reopening be given to sectors that cannot easily work remotely especially those in the production industry who could aid in manufacturing a vaccine.

### Preliminary Insights

Based on BPC’s cross-country analysis, below are eight preliminary insights, along with implications and initial recommendations for the United States.

Criteria for Loosening Social Distancing Interventions – Few countries have explicit transparent quantitative criteria to guide decision-making. In Germany, as mentioned above, the basic reproduction number, or R0, is continuously monitored by the federal and state governments and must be kept under 1 to manage hospital capacity. The Outbreak Management Team, which advises the government of Netherlands on measures that should be met before social distancing interventions are gradually eased, also recommends the R0 should be below 1 for a period of time. It also generally recommends 1) the healthcare system, including ICUs, should be no longer working at or above its capacity and should have had time to recover 2) testing capacity should be sufficient 3) contact tracing capacity should be sufficient to analyze large numbers of data 4) and measurement systems should be available to evaluate the effect of the strategy. In Switzerland, the gradual relaxation of measures depends on criteria including the number of new infections, hospital admissions and deaths, and hospital occupancy rates.

Implications for United States: Guidelines for Opening America Up Again specifies gating criteria based on a downward trajectory of influenza-like illness and COVID-like cases reported within a 14-day period, a downward trajectory of documented cases or percentage of positive tests within a 14-day period, and hospital capacity without crisis care. While some plans recommend a sustained reduction of cases for 14 days, other state plans such as Maryland’s call for first, a reduction in the hospitalization rate, including the current ICU bed usage rate, for COVID-19 patients and second, a reduction in the number of daily COVID-19 deaths. The trajectory of cases or other metrics such as the doubling time of cases may be somewhat limiting until there is a more robust testing infrastructure in place.

Recommendation: States, with the assistance of the federal government, should develop and utilize a uniform and consistent set of quantitative metrics to determine loosening of social distancing interventions that include indicators of epidemic spread, health care capacity, and public health capacity.

Timeframe Between Phases – Various countries have specified time lengths between phases of re-opening the economy. For example, Switzerland, the Czech Republic, and Denmark all plan to allow 2-3 weeks between opening up various sectors (e.g., business, schools).

Implications for United States: The time period between stages in Guidelines for Opening America Up Again are similar to the initial gating criteria: 14-day reduction in symptoms and cases. Some states reportedly are considering shorter timeframes between phases of opening up nonessential businesses.

Recommendation: Given the incubation period of the virus is estimated to be between 2-14 days and the time from presenting symptoms to being tested can range from a few days to over a week, two weeks between phases seem the absolute minimum policymakers should wait to assess the impacts of infection spread prior to further opening up of the economy.

Sequencing Sectors of Economy – Various countries are sequencing the opening of their economy based on the level of risk of transmission in specific sectors. For example, Austria has opened smaller shops and garden centers first with plans to open up bigger shops and malls as early as May, followed by hotels and restaurants the Czech Republic is largely following a similar sequence. Other countries appear to be also taking into account the level of economic importance and disruption to a sector in terms of unemployment. For example, in addition to prioritizing highly automated factories with a low risk of transmission, Germany is considering parts of the manufacturing sector as a priority for opening, given its high value-add to the economy. Spain has also reportedly allowed restarting of construction and manufacturing, although many businesses remain closed. Italy has announced it will begin lifting a nationwide lockdown on May 4 with construction and manufacturing being the first sectors allowed to restart.

Implications for United States: Experts have categorized nonessential businesses based on their contact intensity, number of contacts, and modification potential to allow for social distancing. This should guide policymakers with decisions about opening up various sectors based on risk of transmission.xli Other experts have created frameworks mapping transmission risk by business disruption and recommended prioritizing those sectors with low transmission risk and high business disruption contingent upon occupational safety requirements being met.

Recommendation: Prior to these decisions being made, it is critical that CDC and the Occupational Safety and Health Administration update their guidance for employers to prepare and respond to COVID-19, and it is incumbent that these entities be required to follow the recommended best practices for conducting social distancing.

School Openings – Countries differ with respect to the phases during which school openings might occur, and this is further stratified based on the type of school – primary, secondary, or higher education system. Some experts believe the younger the child, the sooner that schools should re-open since younger children cannot learn autonomously, need more in-person care and support, and depend heavily on schools for their emotional and social development. In addition, younger children who aren’t able to go to school will then need childcare, further complicating the lives of many working parents for example, nurseries in Switzerland did not close at all for this reason during its recent pandemic wave.

Implications for United States: While it appears children are less likely to develop severe COVID-19 infections, there are many outstanding scientific questions with respect to the transmissibility of the virus in children as well as how to best protect high-risk individuals (e.g., older adults, individuals with chronic conditions) who work in a school setting. There is also data to suggest that closing schools may only have a small effect on limiting the spread of COVID-19. Given the school calendar in East Asian countries runs through the summer months, there may be opportunities for the United States to track their experiences.

Recommendation: More research on school closures and guidance on mitigation practices are urgently needed to inform policymakers prior to the start of the 2020-21 school year. Institutions of higher learning should also start preparing and implementing plans to optimize distance learning and ensure the on-campus safety of faculty and staff when public health authorities allow for reopening.

SARS-CoV-2 Testing – Initially, many of the countries analyzed noted difficulty ramping up testing due to a shortage of reagents. With the realization that loosening social distancing interventions is incumbent upon increased testing, more countries are now planning to focus on vulnerable populations beyond just symptomatic patients. For example, Austria recently announced plans to test all personnel and residents of retirement and nursing homes, and Denmark will do the same in the event there is at least one confirmed case of COVID-19 in an institution. Italy’s regional experiences in Lombardy and Veneto demonstrate the importance of testing to both protect vulnerable populations and to limit transmission. Veneto’s significantly lower mortality rate compared to Lombardy is thought to be partially due to its roughly four-times higher testing rate. In addition to testing vulnerable populations, there is an ongoing regional pilot in Veneto conducting testing on essential workers such as supermarket workers, public transportation personnel, and police officers. WHO leaders have publicly stated if the percentage of positive cases are less than 10%, then it is likely a country is testing well.

Implications for United States: The United States is learning from the experiences of other countries. For example, in February, South Korea received global attention for its drive-through screening centers which allowed more people to get tested with less social contact. This has been emulated across various parts of the United States. Nevertheless, most of the countries analyzed currently have higher testing per capita than the United States. According to The COVID Tracking Project, the United States performed about 1.5 million tests in the last week. To replicate Veneto’s successful testing strategy, the United States would have to increase weekly tests to approximately 5 million. Many of the countries analyzed, such as Austria, Denmark, and Netherlands, have a stated goal or capacity that would be equivalent to an average of 4 million tests per week in the United States.

Recommendation: In other words, the immediate priority for the United States should be to triple current SARS-CoV-2 testing capacity in the coming weeks to support the loosening of social distancing interventions. Testing will serve to provide direct protection to vulnerable populations and indirect protection to the community by identifying and mitigating potential transmission hotspots.

Contract Tracing – As described earlier, Germany has provided the most specificity in terms of the number of contract tracers it will require to reduce the spread of COVID-19: five people in public health offices per 20,000 people. During its first pandemic wave, Wuhan, China, required 1,800 contact investigator teams of five people each before the city reopened – approximately one investigator for every 1,200 individuals.

To support contract tracers, Germany, France, and the Netherlands are considering using voluntary mobile apps with Bluetooth technology for contact tracing. All of the East Asian focus countries have used some form of technology-aided contact tracing. Singapore uses a contact-tracing smartphone app – TraceTogether – that identifies people who have been within two meters of a COVID-19 patient for at least 30 minutes for follow up action by contact tracers.

Implications for United States: Experts estimate to begin loosening social distancing interventions, at least 100,00 contact tracers will be needed to rapidly identify contacts of infected individuals and ensure they self-isolate for 14 days this effort would require an estimated \$3.6 billion over 12 months other experts have called for \$12 billion to help expand the contract tracing workforce. The public health infrastructure has been chronically underfunded well before COVID-19 in fact, experts have identified a \$4.5 billion annual gap between what the United States currently spends to build public health capabilities (e.g., surveillance, laboratory capacity, emergency preparedness and response) and what would be required to assure the conditions that people can be healthy. The Public Health Leadership Forum has called on the creation of a new Public Health Infrastructure Fund to address this funding gap.

Recommendation: Congress should address both the short-term contact tracing and long-term infrastructure needs of public health in the next supplemental package to optimally address the COVID-19 pandemic. Partnerships between government and technology companies to develop Bluetooth privacy-protected apps to assist with contract tracing should also be supported and accelerated.

Public Use of Non-Medical Masks – Several of the countries analyzed, such as Austria, the Czech Republic, France, and Germany, are mandating the public wear cloth-based masks particularly in areas where social distancing is not possible such as public transport and grocery stores. The public use of masks has been common across several East Asian countries as well. In phase one of Taiwan’s social distancing measures, if individuals wear face masks properly, the social distancing recommendations can be ignored.

Implications for United States: Limited data exists for the public use of cloth-based masks in preventing the spread of infectious diseases. Concerns include inappropriate wearing of masks, lack of effectiveness due to moisture retention, and a false sense of security that might reduce compliance with social distancing interventions. Nevertheless, the theoretical promise of physically blocking droplets spread from a cough or sneeze particularly in someone otherwise asymptomatic has led to recommendations and in some cases, mandates for their use in public particularly when social distancing is not possible. While the CDC has made such a recommendation, various counties, cities, and states across the United States are now mandating the use of face masks in public or upon entering stores.

Recommendation: Given that this trend will likely continue, the CDC should launch a national awareness campaign to teach Americans best practices with respect to making, donning, doffing, disinfecting, and maintaining cloth-based masks. Central to this campaign must be the key message that masks do not in any way replace personal protective measures or social distancing but rather complement these strategies.

Communication – Winning the public’s trust is critical in any public health crisis. The vice president of Taiwan, also a prominent epidemiologist, provides regular public service announcement broadcasts from the office of the president about key public health aspects of the response. In Switzerland, even though the federal government has introduced relaxations of social distancing measures, the recommendations to the general population are: “Stay at home whenever possible and avoid unnecessary contact. Stay at home and go outside only if it is really necessary. If you are older than 65 or you have some pre-existing condition, then it is strongly recommended that you stay at home unless you need to see a doctor.

Implications for United States: Messaging to the American public from the White House needs to be clear, transparent, and evidence-based with scientific information delivered by the nation’s leading medical experts.

Recommendation: The President’s Coronavirus Guidelines for Americans should not be allowed to expire on April 30 they should be renewed for another month and then updated based on epidemiological data available at that time. These are general recommendations supporting personal protective measures and social distancing that will help Americans slow the spread of the pandemic.

## Covid-19: Is it possible to get to r0 < 1 through social distancing measures? - Biology

By April 2, 2020, >1 million persons worldwide were infected with severe acute respiratory syndrome coronavirus 2. We used a mathematical model to investigate the effectiveness of social distancing interventions in a mid-sized city. Interventions reduced contacts of adults > 60 years of age, adults 20–59 years of age, and children < 19 years of age for 6 weeks. Our results suggest interventions started earlier in the epidemic delay the epidemic curve and interventions started later flatten the epidemic curve. We noted that, while social distancing interventions were in place, most new cases, hospitalizations, and deaths were averted, even with modest reductions in contact among adults. However, when interventions ended, the epidemic rebounded. Our models suggest that social distancing can provide crucial time to increase healthcare capacity but must occur in conjunction with testing and contact tracing of all suspected cases to mitigate virus transmission.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) emerged in Wuhan, China, in December 2019 (1), and in March 2020, the World Health Organization declared coronavirus disease (COVID-19) a pandemic (2). By April 2, 2020, COVID-19 had spread to >181 countries worldwide, and >1 million confirmed cases of COVID-19 and >50,000 deaths had been reported globally (3).

On January 21, 2020, the first case of COVID-19 in the United States was identified in a traveler who had recently returned to Washington from Wuhan (4,5). By March 14, Washington had reported 642 confirmed cases and 40 deaths associated with COVID-19 (6). In response to the rapid spread of the virus, on March 12, 2020, approximately 7 weeks after the first confirmed case in the state, the governor of Washington announced a set of interventions in 3 counties (7,8). More stringent prohibitions were soon imposed, followed by a shelter-in-place order lasting > 6 weeks beginning on March 25, 2020 (9). Similar interventions have been enacted in other US states and in countries in Europe (10,11,12).

We used an epidemic mathematical model to quantify the effectiveness of social distancing interventions in a medium-sized city in the United States or Europe by using Seattle, Washington, as an example. We provide estimates for the proportion of cases, hospitalizations, and deaths averted in the short term and identify key challenges in evaluating the effectiveness of these interventions.

### Methods

Figure 1. Mathematical model illustrating study population divided into 10 age groups and stratified as susceptible (S), exposed (E), infectious (I), and removed (R) from coronavirus disease epidemic. Susceptible persons become exposed at.

We developed an age-structured susceptible-exposed-infectious-removed model to describe the transmission of SARS-CoV-2 (Appendix). We divided the population into 10 age groups: 0–5, 6–9, 10–19, 20–29, 30–39, 40–49, 50–59, 60–69, 70–79, and > 80 years of age. We calibrated the model to the age distribution of the population of the Seattle metropolitan area by using data from the US Census Bureau (13). For each age group, we divided the population into compartments: susceptible (S) for persons who could be infected exposed (E) for persons who have been exposed but are not yet infectious infectious (I) and removed (R) for persons who have recovered or died (Table Figure 1). We only considered symptomatic infections on the basis of estimates that <1% of infections are asymptomatic (15). We assumed only 20% of the cases would be identified because 80% of cases are reported to be mild and would probably be undocumented (16,17). We used previously reported case-fatality and hospitalization rates by age group (16,18). We used the contact matrix for 6 age groups computed by Wallinga et al. (19) and extended it to 10 age groups (Appendix).

We used January 21, 2020, the day the first case was identified in Washington, as the first day of our simulation on the basis of the analysis by T. Bedford (20). By using genomic epidemiology of the first 2 COVID-19 cases identified in Washington, Bedford found that SARS-CoV-2 had been circulating locally for 6 weeks before the second case was identified in the state (20).

We modeled social distancing by reducing the contact rates in an age group for 6 weeks, corresponding to the policy in Washington in mid-March (7,8,21). We divided the population into 3 major groups for social distancing interventions: children, persons < 19 years of age adults 20–59 years of age and adults > 60 years of age.

To quantify the uncertainty around our results, we performed 1,000 simulations varying 3 parameters: the basic reproduction number (R0), the latent period, and the duration of infectiousness (Appendix). For each statistic in the results, we computed the error bars by removing the top and bottom 2.5% of the simulations.

### Results

Estimates for the duration of infectiousness for SARS-CoV-2 range from 5 to 20 days (25 Q. Bi, unpub. data, https://www.medrxiv.org/content/10.1101/2020.03.03.20028423v3). Therefore, we analyzed the influence of the duration of infectiousness on the effectiveness of the social distancing interventions. We kept all other parameters fixed but considered an epidemic with infectious periods of 5, 6, 7, or 8 days, which correspond to the most plausible values (25 Q. Bi, unpub. data, https://www.medrxiv.org/content/10.1101/2020.03.03.20028423v3).

Figure 2. Number of ascertained coronavirus disease cases over 180 days (identified cases over time calculated by mathematical model) using varying infectious periods: A) 5 days B) 6 days C) 7 days D).

In our model, when the infectious period was set to a shorter time of 5 days, the epidemic peaked at 100 days after the introduction of the first case. As we extended the infectious period, the epidemic took much longer to take off (Figure 2) because we kept a fixed R0, so that a longer infectious period implied a smaller infectious rate. When we used the longest infectious period of 8 days, we noted the epidemic peaked 128 days after the first case was introduced. Therefore, early interventions delay the epidemic but do not substantially change the pool of susceptible persons, which allows similar-sized epidemics to occur later (Figure 2).

We then considered the delay of the epidemic under the 4 social distancing interventions and different infectious periods (Figure 2). As expected, the fourth social distancing strategy, the one applied to all age groups, delayed the epidemic the longest, >50 days, compared with a baseline of using no interventions. Targeting adults > 60 years of age and children delayed the epidemic by ≈10 days, regardless of infectious period. Targeting adults <60 and > 60 years of age delayed the epidemic by 41 days when we set the infectious period to 8 days and delayed it 39 days when we set the infectious period to 5 days. Social distancing of only adults > 60 years of age only delayed the epidemic by 2 days, regardless of infectious period (Appendix Table 1). The infectious period did not substantially affect the peak epidemic height compared with baseline.

Figure 3. Number of ascertained coronavirus disease (identified cases over time calculated by mathematical model) with adults reducing their contact by 25% (A, B) 75% (C, D) and 95% (E, F). We used.

We examined the effectiveness of the 3 social distancing interventions in adults and the timeframe in which interventions began. We considered social distancing interventions starting 50 days (Figure 3, panels A, C, E) and 80 days (Figure 3, panels B, D, F) after the first case was identified and reduction in adult contacts by 25% (Figure 3, panels A, B), 75% (Figure 3, panels C, D), and 95% (Figure 3, panels E, F). We found that the effect of interventions was dramatically different when started early in the epidemic curve, before the exponential phase of the epidemic, rather than later.

When we started interventions on day 50, we saw a delay in the epidemic regardless of the level of reductions in contact in the adult population, with little change in the magnitude of the epidemic peak. In comparison, when we began the interventions later, during the exponential phase of the epidemic, all interventions flattened epidemic curve. The strategy of reducing the contacts only of adults > 60 years of age resulted in a moderate reduction of 5,000 (21%) fewer cases at the epidemic peak compared with baseline. Limiting contact for adults > 60 years of age, as expected, is the only intervention for which there was minimal rebound after the intervention was lifted (Figure 3, panels B, D, F) because older adults make up only 16% of the population and have substantially fewer contacts than the other age groups.

We found that the strategy targeting adults > 60 years of age and children resulted in 10,500 (45%) fewer cases than baseline at the epidemic peak (Figure 3, panels B, D, F), emphasizing the fact that children are the age group with the highest number of contacts in our model. By comparison, when we applied the adults-only strategy, we saw 11,000 (47%) fewer cases than baseline at the epidemic peak for 25% reduction in contacts in adults <60 years of age (Figure 3, panel B). When we reduced contact by 75% in this age group, the peak epidemic cases dropped by 21,000 (91%). When we reduced contact by 95% in this age group, we noted 22,500 (98%) fewer cases (Figure 3, panels D, F), and the epidemic curve grew at a slower rate in both instances. Of the 4 intervention scenarios, the strategy involving all age-groups decreased the epidemic peak the most and showed the slowest growth rate, which we expected because contacts in all age groups are reduced. Even when we used a lower reduction in contacts of 25% in adults <60 years of age, we noted 16,000 (69%) fewer cases at the epidemic peak (Figure 3, panel B). With higher reduction in contacts (95%) in adults <60 years of age, the strategy involving all age groups mitigated nearly all cases at the epidemic peak (Figure 3, panel F). However, our results suggest that all interventions can result in new epidemic curves once the interventions are lifted.

Figure 4. Proportion of coronavirus disease cases, hospitalizations, and deaths averted during 100 days for various social distancing scenarios in which adults reduce their contact by 25% (A–C) 75% (D–F) and 95% (G–I).

Next, we considered the effects of social distancing interventions over the first 100 days of the epidemic and assumed that the social distancing interventions started on day 50, which corresponds to the approximate date when social distancing interventions started in Washington. To investigate the sensitivity of the model to the chosen parameters, we ran 1,000 simulations (Appendix). We obtained curves that varied widely for both the number of cases and the duration and timing of the epidemic (Appendix Figures 1–3). We ran simulations with the mean parameter values (R0 = 3, an infectious period lasting 5 days, and a latent period of 5.1 days). We then observed the number of cases and proportion of cases, hospitalizations, and deaths averted during the first 100 days. We noted that reducing the contacts of adults > 60 years of age averted only 18% of cases for the whole population (Figure 4) but averted 50% of cases for this age group (Appendix Figure 4). In addition, this intervention reduced the overall number of hospitalizations by 30% and reduced deaths by 39% for the whole population (Figure 4) and hospitalizations and deaths by > 49% for the adults > 60 years of age (Appendix Figures 5, 6). Adding a social distancing intervention in children slowed the epidemic curve (Figure 3) and reduced the overall hospitalizations by > 64% (Figure 4) and by > 53% across all age groups (Appendix Figures 5, 6).

### Discussion

The term “flatten the curve,” originating from the Centers for Disease Control and Prevention (26), has been used widely to describe the effects of social distancing interventions. Our results highlight how the timing of social distancing interventions can affect the epidemic curve. In our model, interventions put in place and lifted early in the epidemic only delayed the epidemic and did not flatten the epidemic curve. When an intervention was put in place later, we noted a flattening of the epidemic curve. Our results showed that the effectiveness of the intervention will depend on the ratio of susceptible, infected, and recovered persons in the population at the beginning of the intervention. Therefore, an accurate estimate of the number of current and recovered cases is crucial for evaluating possible interventions. As of April 2, 2020, the United States had performed 3,825 tests for SARS-CoV-2 per 1 million population (27). By comparison, Italy had performed 9,829 tests/1 million population (27). Expanding testing capabilities in all affected countries is critical to slowing and controlling the pandemic.

Some evidence suggests that persons who recover from COVID-19 will develop immunity to SARS-CoV-2 (28). However, at this point the duration of immunity is unclear. If immunity lasts longer than the outbreak, then waning immunity will not affect the dynamics of the epidemic. Furthermore, persons who recover from COVID-19 could re-enter the workforce and help care for the most vulnerable groups. However, if immunity is short-lived, for instance on the order of weeks, persons who recover could become re-infected, and extensions to social distancing interventions might be necessary.

We used a mathematical model to quantify short-term effectiveness of social distancing interventions by measuring the number of cases, hospitalizations, and deaths averted during the first 100 days under 4 social distancing intervention scenarios and assuming different levels of reduction in the contacts of the adult population. When we investigated the short-term effects of social distancing interventions started early in the epidemic, our models suggest that the intervention involving all age groups would consistently decrease the number of cases considerably and delay the epidemic the most. Of note, with > 25% reduction in contact rates for the adult population, combined with 95% reduction in older adults, the number of hospitalizations and deaths could be reduced by >78% during the first 100 days, a finding that agrees with previous reports (29,30).

Our results must be interpreted with caution. Hospitalizations and deaths averted during the first 100 days in our model would likely occur later if the interventions are lifted without taking any further action, such as widespread testing, self-isolation of infected persons, and contact tracing. As in any model, our assumptions could overestimate the effect of the interventions. However, quantifying the short-term effects of an intervention is vital to help decision makers estimate the immediate number of resources needed and plan for future interventions.

Our simulations suggest that even in the more optimistic scenario in which all age groups reduce their contact rates by > 85%, the epidemic is set to rebound once the social distancing interventions are lifted. Our results suggest that social distancing interventions can give communities vital time to strengthen healthcare systems and restock medical supplies, but these interventions, if lifted too quickly, will fail to mitigate the current pandemic. Other modeling results also have suggested that extended periods of social distancing would be needed to control transmission (18). However, sustaining social distancing interventions over several months might not be feasible economically and socially. Therefore, a combination of social distancing interventions, testing, isolation, and contact tracing of new cases is needed to suppress transmission of SARS-CoV-2 (31,32). In addition, these interventions must happen in synchrony around the world because a new imported case could spark a new outbreak in any given region.

Our results suggest that the SARS-CoV-2 infectious period has an extraordinary influence in the modeled speed of an epidemic and in the effectiveness of the interventions considered. However, current estimates of the infectious period range from 5 to 20 days (25 Q. Bi, unpub. data, https://www.medrxiv.org/content/10.1101/2020.03.03.20028423v3). Of note, all estimates of the infectious period were made on the basis of PCR positivity, which does not necessarily translate to viability or infectivity of the virus (33). We urgently need studies to definitively define the duration of infectiousness of SARS-CoV-2.

Our work has several limitations and should be interpreted accordingly. First, deterministic mathematical models tend to overestimate the final size of an epidemic. Further, deterministic models always will predict a rebound in the epidemic once the intervention is lifted if the number of exposed or infectious persons is >0. To avoid that problem, we forced our infected compartments to 0 if they had <1 person infected at any given time. Second, we considered the latent period to be equal to the incubation period, but others have suggested that presymptomatic transmission is occurring (L. Tindale, unpub. data, https://www.medrxiv.org/content/10.1101/2020.03.03.20029983v1) and SARS-CoV-2 is shed for a prolonged time after symptoms end (34). Whether virus shed by convalescent persons can infect others currently is unclear. Further, we considered that mild and severe cases would be equally infectious and our model could be overestimating the total number of infections, which would amplify the effect of social distancing interventions. We also considered infected children and adults to be equally infectious, and our model could be overestimating the effect of social distancing in persons < 19 years of age. Strong evidence suggests that children have milder COVID-19 symptoms than adults and might be less infectious (23). More studies are needed clarify the role children play in SARS-CoV-2 transmission. In our models, we assumed death and hospitalization rates would be similar to those experienced in Wuhan, where older age groups have been the most affected. Because different countries have different population structures and different healthcare infrastructure, including varying numbers of hospital beds, ventilators, and intensive care unit beds, effects of social distancing interventions could vary widely in different places.

Our results align with an increasing number of publications estimating the effects of interventions against COVID-19. Several researchers have investigated how social distancing interventions in Wuhan might have affected the trajectory of the outbreak (30,35,36 J. Zhang, unpub. data, https://www.medrxiv.org/content/10.1101/2020.03.19.20039107v1). Others have investigated the effect of similar measures elsewhere and concluded that social distancing interventions alone will not be able to control the pandemic (37,38 M.A. Acuña-Zegarra, unpub. data, https://www.medrxiv.org/content/10.1101/2020.03.28.20046276v1 N.G. Davies, unpub. data, medrxiv.org/content/10.1101/2020.04.01.20049908v1 S. Kissler, unpub. data, https://www.medrxiv.org/content/10.1101/2020.03.22.20041079v1).

Taken together, our results suggest that more aggressive approaches should be taken to mitigate the transmission of SARS-CoV-2. Social distancing interventions need to occur in tandem with testing and contact tracing to minimize the burden of COVID-19. New information about the epidemiologic characteristics of SARS-CoV-2 continues to arise. Incorporating such information into mathematical models such as ours is key to providing public health officials with the best tools to make decisions in uncertain times.

Dr. Matrajt is a research associate at the Fred Hutchinson Cancer Research Center. Her research interests include using quantitative tools to understand infectious disease dynamics and to optimize public health interventions.

Dr. Leung is a postdoctoral research fellow at the Fred Hutchinson Cancer Research Center. Her research interests include using mathematics to understand infectious disease transmission.

## Introduction

The spread of infectious diseases is determined by two factors: the physical and chemical characteristics of the virus, and the social network that defines the structure of contact among people. Humans are not just hosts for viruses. They are actively involved in social contact with others and, as a result, spread the viruses to not just anyone but more or less socially predictable subjects. How humans form social networks affects the overall state and structure of the spread of infection. The current article focuses on this second aspect, that is, social networks. We measure the out-degree distribution of the COVID-19 transmission network in South Korea and predict its function, which allowed us to examine the implications of transmission network information in terms of policy responses to COVID-19, and provides a better informed interpretation of the various reproduction numbers.

Although it is widely known that the characteristics of virus transmission networks are an important determinant of the size and condition of outbreaks, such evidence has been highly limited in policy-making and research on COVID-19, making it challenging to implement evidence-based policies for transmission networks. Social distancing is one such example. Despite the fact that there are local structures for the entire transmission network that disproportionately contribute to the spread of infection, social distancing policies recommend or enforce decreased contact among all members of society. Because this recommendation is not based on scientific analysis of the spread network, the policy may be considered less than efficient or effective.

This lack of scientific examination of transmission networks also limits the interpretation of major indicators of infection, which may lead to inefficient and/or ineffective policies. One important example is the calculation and interpretation of various reproduction numbers (e.g., R, R0). R is an indicator which governmental authorities heavily rely on to determine the current state and future risks of viral infection transmission for quarantine and isolation. However, an estimation process of this indicator suggests that it does not evaluate structural characteristics of the viral transmission network, such as skewness of contact opportunities, thus leading to occasional failures in providing reliable information, which is important for decision-making on resource distribution to control the outbreak.

R is the product of the transmission rate (infection-producing contacts per unit time) and infectious period. To obtain each item, for example, a transmission rate, we assume a model for the infection process (e.g., SIR, SEIHR) and estimate the model's parameters using the number of people at each stage and the rate at which that number increases and decreases. The transmission rate is one of these estimated model parameters 1 . This type of estimation assumes that the transmission rate is determined by the proportion of people at each stage, its rate of increase and decrease, and the rest of the parameters (isolation rate, recovery rate, etc.), which overlook the impact of the transmission network structure. However, the transmission network structure can affect the transmission rates. Even if the proportion of people in each stage and the other parameters are the same, the transmission rate may vary depending on the infection network structure to which people belong.

Meyer et al.'s research is a good example of the impact of network structure. Meyer et al. pointed out that outbreaks under the same R0 (basic reproduction number) can be very different depending on the distribution of out-degrees, the latter meaning the number of transmissions made by each infected person 2 . They compared the power-law distribution, the extreme right-skewed distribution often observed in network measures, to a more moderate Poisson distribution. Though they are expressed by the same R0, the outbreak becomes much more serious if the out-degree follows a Poisson distribution. In contrast, the outbreak may not be as serious if the out-degree follows a power-law distribution because it is likely that a very small number of super-spreaders lead us to overestimate patient increasing rate and R0. By the same logic, the same R0 under a Poisson distribution might suggest that the virus has spread more evenly to the overall population. This result implies that the interpretation of R0, without considering the characteristics of transmission networks, might be incomplete.

The effect of transmission networks on the spread of infection is only theoretically acknowledged, while scientific evidence is absent from current COVID-19 policies. We are not the first to point this out. Existing research have raised the same concerns. However, most previous studies did not address real-world transmission networks between humans. Most existing research deal with networks on social media (e.g., Twitter) 3,4,5,6 or utilize virtual network data 2, 7 . While there are a small number of studies that use real-world network data, they deal with connections between genomes 8 or contain institutions or organizations in the transmission network's nodes set 9 . That is, technically speaking, they cannot be seen as a network that can demonstrate the transmission dynamics between people. These limitations are understandable given the scarcity of empirical transmission networks between humans. However, we strongly recommend collecting and analyzing empirical network data among humans if we want COVID-19 policies to closely reflect the realities and feasibility between cost and benefit. Therefore, we collected and analyzed real-world transmission network data from people in Korea.

The case of South Korea provides an interesting avenue for this research for two reasons. First, transmission data between humans exists in South Korea. South Korea is famous for active contact tracing 10 . The Infectious Disease Control and Prevention Act (in Korean, 감염병의 예방 및 관리에 관한 법률) in Korea mandates the disclosure of information about confirmed patients, including "movement paths, transportation means, medical treatment institutions, and contacts of patients with the infectious disease" 11 . In compliance with this law, information on infection routes are consistently collected from the initial stage and publicly disclosed on local government websites. By collecting and combining these pieces of information, we can construct the whole network data among humans for the spread of COVID-19 in South Korea. It is a rare opportunity worldwide and is also the first reason we decided to use Korean data.

Second, South Korea has thus far controlled the spread of COVID-19 without relying on strict lockdown policies such as stay-at-home orders or mobility restrictions nationwide. This allowed us to evaluate the structural characteristics and their impact on transmission, while it is less distorted by policy measures that affect naturally existing social ties. Therefore, an analysis of South Korea's infection network is a good reference point for many countries that want effective and efficient epidemic policy through moderate control. We derived several network indicators and their distributions for real transmission data from South Korea, thereby seeking possibilities for improving the efficiency and efficacy of the current policies to curb the COVID-19 outbreak.

More specifically, we attempt to answer the following research questions:

What are the characteristics of the COVID-19 transmission network in South Korea?

What are the implications of the distribution of the COVID-19 transmission network index in South Korea from policy and research perspectives?

## The Effects of Physical Isolation on the Pandemic Quantified

###### Apr 10, 2020

ABOVE: A playground in Maumee, Ohio, where the governor’s stay-at-home order went into effect March 23
SHAWNA WILLIAMS

I n July 2008, some 400 young people from the Solomon Islands visited Sydney, Australia, for a Catholic youth festival. Short on accommodations—the week-long event drew 223,000 pilgrims from across the world—the Solomon Islanders bedded down in the cavernous gym of a local school. Within days, a spate of fever, headaches, and coughing fits signaled to organizers that they had a serious problem. An influenza outbreak had ripped through the closely quartered group, eventually making more than one-fourth of them unwell.

A large group of Australians were also staying at the school and passing around the virus. But far fewer of them became ill—just 27 of the 255. What protected them?

In turned out the Australians had slept in groups of eight, each isolated in their own classroom.

Health officials treated everyone and mopped up the Sydney outbreak within a week or so. But that limited incident had a lasting impact on the infectious disease community. Written up as a study three years later in an obscure Australian government journal called Communicable Disease Intelligence, it’s one of the few proven examples of the benefits that social and physical distancing measures can have against a contagious virus. As such, it’s a key part of what researchers at the Centre for Evidence-Based Medicine at the University of Oxford admit is “limited” evidence available to support social-distancing measures as a response to the ongoing pandemic. Alongside studies of how different cities dealt with the 1918 flu pandemic that killed millions of people around the world, all those sick worshippers camped out in a school are part of the reason you are in lockdown.

Google data from smart phone users show that visits to shops, museums, and cafes in the UK have fallen by 85 percent.

Social distancing worked then. So how is it working now to contain the ongoing COVID-19 pandemic? The answer comes down to two questions: Are people behaving as they are expected to? And do those behavioral changes subsequently reduce transmission of the disease as predicted?

On the first, Mirco Tonin, an economist at the Free University of Bozen-Bolzano in Italy, has asked nearly 900 people in the country about their lockdown behavior in recent weeks. His results indicate most people are complying with requests to stay at home. Or at least about half the people who responded to the survey say that’s what they are doing. Although Tonin is usually suspicious of data from self-reported surveys on wrong-doing, in this case, he tends to believe the respondents.

“If you ask people about tax evasion you get zero and that’s clearly not true. If you ask if they cheat on their husbands or wives, then they don’t like to admit it,” he tells The Scientist. “But here we were asking, are you meeting your friends, are you meeting your relatives, and those are behaviors that are socially acceptable. So people were probably more likely to admit they were doing it.”

Stefan Pfattheicher, a psychologist at Aarhus University in Denmark, surveyed more than 2,000 people across the UK, US, and Germany in mid-March and got similar results. “More than 50 percent of all participants say they do the maximum asked of them,” he says. And questionnaires in China show that citizens of Wuhan and Shanghai reported between seven and nine times fewer daily contacts with other people than was typical.

Other data support the conclusion that people are staying at home. Earlier this month, Google released location data harvested (and anonymized) from smart phone users across the world. They show, for example, that visits to shops, museums, and cafes in the UK have fallen by 85 percent. In the US, such activity has dropped by 47 percent.

The second question—how much does all this social distancing reduce transmission—is harder to answer with real data. That’s because there’s typically a three-week lag between infection and people dying, which, without comprehensive testing, remains the most reliable indicator of disease spread.

Researchers in Hong Kong have tried to address this dearth of data using a statistical trick called “nowcasting” to estimate a real-time measure of how the virus is spreading. Called effective reproduction number (Rt), it’s a variation on the much-discussed R0 (basic reproduction number) used to indicate on average how many people will catch the disease from an infected individual.

Gabriel Leung, an epidemiologist at the University of Hong Kong, says Rt is a more reliable measure than R0 because it varies according to control measures that are put in place to drive down transmission such as social distancing. R0 is an average of recorded case data, which shows previous infections rather than what’s happening now, as Rt attempts to do. Data published by his group shows that the Rt in Hong Kong has dropped to about 0.7 after hovering closer to 1 for much of March. If sustained, that would indicate the epidemic there is in decline. “It coincides with the much stricter physical distancing measures that Hong Kong has put in place,” Leung said at a media briefing in London this week.

Developing a new lifestyle with more distance is a challenge we’re going to have to face.

Other researchers have used computer models to show that early introduction of social distancing can explain lower infection and death rates now seen in places such as China. Among the harshest restrictions in place across the world, the Chinese authorities banned people in some regions from leaving their homes, even to buy food and medicine.

Marco Ajelli, an infectious-disease expert at the Bruno Kessler Foundation in Trento, Italy, who was a member of the team that carried out the surveys in Shanghai and Wuhan, says his team’s model shows that “the social distancing measures adopted in China were sufficient to control the epidemic.” The results of other models, including one from researchers in Germany published in Science this week, support that conclusion.

Strict lockdown measures are also credited with helping Australia and New Zealand to suppress the spread of the virus so far, aided by both countries shutting their borders to international visitors early on.

There is more uncertainty over the effect of closing schools. Ajelli says his model showed that “school closures alone are not enough to contain the epidemic. Additional stricter measures, similar to those implemented in China, are needed.” Separate research from University College London also concludes that the evidence to support the closure of schools to combat COVID-19 is “very weak.”

### See “Study Questions if School Closures Limit the Spread of COVID-19”

As the weeks drag on, such studies are vital to determine when locked-down communities could be allowed out again—and with what restrictions. “We now have a real challenge for social distancing because people are getting really tired of it,” Sung-il Cho, an epidemiologist at Seoul National University in South Korea, said during the London briefing. “Any weakening of the social distancing could mean a new surge [in infection] because in Korea the regular lifestyle is pretty close. Developing a new lifestyle with more distance is a challenge we’re going to have to face.”

## Results

Across all nine scenarios, for varying proportion of symptomatic cases and infectiousness period, the model was calibrated to closely match the NEL observed data (Figure S1 in the supplementary material). All fitted parameters are summarised in Table S3 of the supplementary material.

Figure 3 shows the model-projected daily cases, cumulative deaths and daily number of hospitalised patients for varying levels of daily contacts per person (or daily contact rate), c, for a population-average infectiousness period of 5 days and a proportion of symptomatic infection of 70%. Our results suggest that significant relaxation of social distancing measures in NEL, with an average of more than 6 daily contacts per person from 4th July 2020 leads to a resurgence of COVID-19 cases and a secondary epidemic wave (Fig. 3d–f). The size of a secondary COVID-19 wave depends on the level of social distancing compliance, i.e. on the average number of daily contacts per person.

Projections of the mathematical model forecasting the number of COVID-19 cases (left panels), deaths (centre panels) and hospitalised patients (right panels) for varying numbers of daily contacts, c. (a)–(c) show high levels of social distancing, c = 3 to 6, and (d)–(f) show low social distancing, c = 7 to 12. Infectiousness period = 5 days, proportion of symptomatic infections = 70%. Estimates for hospital capacity levels are given in (f) for reference.

With full relaxation of social distancing and return to pre-COVID-19 levels of social contact (c ≈ 11), a secondary COVID-19 wave may occur up to 8 times larger than the original wave in terms of number of infections (Fig. 3d), peak number of patients hospitalised with COVID-19 and associated deaths (Figs. 3f, 4b). In addition to a surge in the number of daily cases, hospitalised patients and deaths, the health and care demand will exceed the acute bed capacity in NEL in this scenario.

Cumulative number of COVID-19 cases (a), hospital discharges and deaths associated with COVID-19 (b) and hospitalised patients with COVID-19 (c) for different levels of compliance with social distancing quantified by the number of daily contacts, c, from 4 July 2020. The cumulative totals for 2020 are considered, including forecasts up to 31 December 2020. For c > 6 the number of cases, deaths, hospitalised patients and discharges increase significantly. The results shown here assume an infectiousness period of 5 days and that symptomatic infections comprise 70% of all infections.

At the time of submission, analysis suggested that a secondary COVID-19 wave, including excess demand on acute care, may be prevented when a sufficient level of social distancing remains in place. Specifically, to prevent a significant secondary wave in NEL, the average daily contact rate after July 04 must not exceed 6 (Fig. 3a–c). With this level of compliance with social distancing, the burden from COVID-19 would be less in terms of total cases, hospitalised patients and deaths (Fig. 4a–c), and the acute bed capacity demand not exceeded (Fig. 5a,b) and Re will remain below 1 (Fig. 5c,d). Hence avoiding a secondary wave of COVID-19 in NEL would require reduction in pre-COVID-19 average daily contact rate to around 50% of its pre COVID-19 level in the region indefinitely in the near term. While our analysis examined the period up to early 2021 only, the principle of our analysis remain the same for looking further forwards in time—future epidemic waves require Re < 1 for suppression, which in our results corresponds to an average daily contact rate of up to 6.

Predicted size of the secondary COVID-19 wave (black lines), measured by the peak in all COVID-19 hospitalised patients (left panels) and critical care COVID-19 hospitalised patients (right panels) for different levels of compliance with social distancing from 4 July 2020 as a function of the daily number of contacts, c, (top row) and the effective reproduction number, Re (on 5 July 2020, bottom row). Estimates for hospital capacity levels (coloured lines) are given for reference. For c > 6, Re is above 1 and a secondary wave is predicted. The results shown here assume an infectiousness period of 5 days and that symptomatic infections comprise 70% of all infections.

A secondary wave remains within the bed capacity of the health and care system for an average number of daily contacts per person of up to 7 to 8 (Fig. 5a,b). However, this scenario is associated with a significantly increased numbers of total cases, hospitalised patients, discharges and deaths (Fig. 5). A daily contact rate of 8 gives an end-of-year death total of over 4000, a more than threefold increase compared to if daily contacts were kept to 6 or lower. Going from a population average rate of daily contacts of 8 to 9 increases the peak in COVID-19 hospitalised patients from 2500 to 4200, crossing all 3 overall bed capacity scenarios, including the maximum capacity (current plus planned plus Nightingale) of approximately 2900 beds (Fig. 3).

When we vary the infectiousness period to be 3 or 1 days, and the proportion of symptomatic infection to be 50% or 25%, the overall results remain consistent, with a secondary epidemic wave present unless restricted social distancing is present. Across all 9 scenarios, for varying levels of infectiousness period and proportion of symptomatic infection, the limit on the average number of daily contacts to suppress a secondary wave is between 5 and 6, while the maximum average number of contacts for a secondary peak to remain within NEL capacity levels is between 8 (in 7 scenarios) and 9 (in 2 scenarios). Across scenarios, a longer infectiousness period pushes a secondary wave further into the future, and a lower proportion of symptomatic infections leads to a smaller peak in hospitalised patients for equivalent c values. Therefore, we find it is the balance between infectiousness period and the proportion of infections that are symptomatic that controls the timing and the strength of a potential secondary wave in NEL. Results for all 9 scenarios are summarised in Figures S1–S12 of the supplementary material.

## On-off social distancing may be needed until 2022: Harvard study

Effects of depletion of susceptibles and seasonality on the effective reproduction number by strain and season. Estimated multiplicative effects of HCoV-HKU1 incidence (red), HCoV-OC43 incidence (blue), and seasonal forcing (gold) on weekly effective reproduction numbers of HCoV-HKU1 (top panels) and HCoV-OC43 (bottom), with 95% confidence intervals. The black dot (with 95% confidence interval) plotted at the start of each season is the estimated coefficient for that strain and season compared to the 2014-15 HCoV-HKU1 season. The seasonal forcing spline is set to 1 at the first week of the season (no intercept). On the x-axis, the first “week in season” corresponds to epidemiological week 40. Credit: Science (2020). DOI: 10.1126/science.abb5793

A one-time lockdown won't halt the novel coronavirus and repeated periods of social distancing may be required into 2022 to prevent hospitals from being overwhelmed, Harvard scientists who modeled the pandemic's trajectory said Tuesday.

Their study comes as the US enters the peak of its COVID-19 caseload and states eye an eventual easing of tough lockdown measures.

The Harvard team's computer simulation, which was published in a paper in the journal Science, assumed that COVID-19 will become seasonal, like closely related coronaviruses that cause the common cold, with higher transmission rates in colder months.

But much remains unknown, including the level of immunity acquired by previous infection and how long it lasts, the authors said.

"We found that one-time social distancing measures are likely to be insufficient to maintain the incidence of SARS-CoV-2 within the limits of critical care capacity in the United States," lead author Stephen Kissler said in a call with reporters.

"What seems to be necessary in the absence of other sorts of treatments are intermittent social distancing periods," he added.

Widespread viral testing would be required in order to determine when the thresholds to re-trigger distancing are crossed, said the authors.

Transmission model fits for HCoV-OC43 and HCoV-HKU1. (A) Weekly percent positive laboratory tests multiplied by percent influenza-like illness (ILI) for the human betacoronaviruses HCoV-OC43 (blue) and HCoV-HKU1 (red) in the United States between 5 July 2014 and 29 June 2019 (solid lines) with simulated output from the best-fit SEIRS transmission model (dashed lines). (B and C) Weekly effective reproduction numbers (Re) estimated using the Wallinga-Teunis method (points) and simulated Re from the best-fit SEIRS transmission model (line) for HCoVs OC43 and HKU1. The opacity of each point is determined by the relative percent ILI multiplied by percent positive laboratory tests in that week relative to the maximum percent ILI multiplied by percent positive laboratory tests for that strain across the study period, which reflects uncertainty in the Re estimate estimates are more certain (darker points) in weeks with higher incidence. Credit: Science (2020). DOI: 10.1126/science.abb5793

The duration and intensity of lockdowns can be relaxed as treatments and vaccines become available. But in their absence, on and then off distancing would give hospitals time to increase critical care capacity to cater for the surge in cases that would occur when the measures are eased.

"By permitting periods of transmission that reach higher prevalence than otherwise would be possible, they allow an accelerated acquisition of herd immunity," said co-author Marc Lipsitch.

Conversely, too much social distancing without respite can be a bad thing. Under one modeled scenario "the social distancing was so effective that virtually no population immunity is built," the paper said, hence the need for an intermittent approach.

The authors acknowledged a major drawback in their model is how little we currently know about how strong a previously infected person's immunity is and how long it lasts.

Invasion scenarios for SARS-CoV-2 in temperate regions. These plots depict the prevalence of SARS-CoV-2 (black, cases per 1,000 people), HCoV-OC43 (blue, % positive multiplied by % ILI), and HCoV-HKU1 (red, % positive multiplied by % ILI) for a representative set of possible pandemic and post-pandemic scenarios. The scenarios were obtained by varying the cross immunity between SARS-CoV-2 and HCoVs OC43/HKU1 (χ3X) and vice-versa (χX3), the duration of SARS-CoV-2 immunity (1/σ3), and the seasonal variation in R0 (f), assuming an epidemic establishment time of 11 March 2020 (depicted as a vertical grey bar). Parameter values used to generate each plot are listed below all other parameters were held at the values listed in table S8. (A) A short duration (1/σ3 = 40 weeks) of SARS-CoV-2 immunity could yield annual SARS-CoV-2 outbreaks. (B) Longer-term SARS-CoV-2 immunity (1/σ3 = 104 weeks) could yield biennial outbreaks, possibly with smaller outbreaks in the intervening years. (C) Higher seasonal variation in transmission (f = 0.4) would reduce the peak size of the invasion wave, but could lead to more severe wintertime outbreaks thereafter [compare with (B)]. (D) Long-term immunity (1/σ3 = infinity) to SARS-CoV-2 could lead to elimination of the virus. (E) However, a resurgence of SARS-CoV-2 could occur as late as 2024 after a period of apparent elimination if the duration of immunity is intermediate (1/σ3 = 104 weeks) and if HCoVs OC43/HKU1 impart intermediate cross immunity against SARS-CoV-2 (χ3X = 0.3). (A) χ3X = 0.3, χX3 = 0, 1/σ3 = 40 weeks, f = 0.2. (B) χ3X = 0.7, χX3 = 0, 1/σ3 = 104 weeks, f = 0.2. (C) χ3X = 0.7, χX3 = 0, 1/σ3 = 104 weeks, f = 0.4. (D) χ3X = 0.7, χX3 = 0, 1/σ3 = infinity, f = 0.2. (E) χ3X = 0.3, χX3 = 0.3, 1/σ3 = 104 weeks, f = 0.4. Credit: Science (2020). DOI: 10.1126/science.abb5793

Virus likely here to stay

At present the best guesses based on closely-related coronaviruses are that it will confer some immunity, for up to about a year. There might also be some cross-protective immunity against COVID-19 if a person is infected by a common cold-causing betacoronavirus.

One thing however is almost certain: the virus is here to stay. The team said it was highly unlikely that immunity will be strong enough and last long enough that COVID-19 will die out after an initial wave, as was the case with the SARS outbreak of 2002-2003.

Antibody tests that have just entered the market and look for whether a person has been previously infected will be crucial in answering these vital questions about immunity, they argued, and a vaccine remains the ultimate weapon.

Outside experts praised the paper even as they emphasized how much remained unknown.

One-time social distancing scenarios in the absence of seasonality. (A to E) Simulated prevalence of COVID-19 infections (solid) and critical COVID-19 cases (dashed) following establishment on 11 March 2020 with a period of social distancing (shaded blue region) instated two weeks later, with the duration of social distancing lasting (A) four weeks, (B) eight weeks, (C) twelve weeks, (D) twenty weeks, and (E) indefinitely. There is no seasonal forcing R0 was held constant at 2.2 (see fig. S12 for R0 = 2.6). The effectiveness of social distancing varied from none to a 60% reduction in R0. Cumulative infection sizes are depicted beside each prevalence plot (F to J) with the herd immunity threshold (horizontal black bar). Of the temporary distancing scenarios, long-term (20-week), moderately effective (20%-40%) social distancing yields the smallest overall peak and total outbreak size. Credit: Science (2020). DOI: 10.1126/science.abb5793

"This is an excellent study that uses mathematical models to explore the dynamics of COVID-19 over a period of several years, in contrast to previously published studies that have focused on the coming weeks or months," Mark Woolhouse, an infectious disease epidemiologist at the University of Edinburgh said.

"It is important to recognize that it is a model it is consistent with current data but is nonetheless based on a series of assumptions—for example about acquired immunity—that are yet to be confirmed."

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