Effective Reproductive Rate

Public health measures and

the reproduction number of SARS-CoV-2

Thomas V. Inglesby*

May 1, 2020

Coronavirus disease 2019 (COVID-19) is a respiratory infectious disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), first detected in early December 2019 in Wuhan, China. It has since spread throughout the world.

One measure of viral spread is the R₀, the expected number of secondary infectious cases produced by a primary infectious case. This calculation is used to determine the potential for epidemic spread in a susceptible population. The effective reproduction number, R_t, determines the potential for epidemic spread at a specific time t under the control measures in place (Figure 1). To evaluate the effectiveness of public health interventions, the R_t should be quantified in different settings, ideally at regular and frequent intervals (eg, weekly).

Figure 1. Concepts of the Effective Reproduction Number

In an article published in JAMA, Pan and colleagues¹ evaluated the association of public health interventions with the epidemiological features of the COVID-19 outbreak in Wuhan by 5 periods, according to key events and interventions, including cordons sanitaire, traffic restriction, social distancing, home confinement, centralized quarantine, and universal symptom survey.

In their study, Pan et al¹ determined the R_t as an indicator to measure the transmission of SARS-CoV-2 before and after the interventions. In a figure in their article, the authors show the extraordinary change in the rate of transmission of SARS-CoV-2 associated with reducing social interaction (Figure 2). In early through mid-January 2020, the SARS-CoV-2 epidemic in Wuhan had an R_t of 3 to 4. In other words, each case spread to an average of 3 to 4 others. That is a striking number: compare it to the R_t of 1.4 to 1.7 for influenza, which is a disease that spreads widely around the world every year. Couple that with the fact that each new generation of SARS-CoV-2 cases occurs every 5 days, and it is clear to see how this epidemic was spreading out of control.

Figure 2. The Effective Reproduction Number (R_t) Estimates Based on Laboratory-Confirmed Coronavirus Disease 2019 (COVID-19) Cases in Wuhan, China

The effective reproduction number R_t is defined as the mean number of secondary cases generated by a typical primary case at time t in a population, calculated for the whole period over a 5-day moving average. Results are shown since January 1, 2020, given the limited number of diagnosed cases and limited diagnosis capacity in December 2019. The darkened horizontal line indicates R_t = 1, below which sustained transmission is unlikely so long as antitransmission measures are sustained, indicating that the outbreak is under control. The 95% credible intervals (CrIs) are presented as gray shading.

From Pan et al.¹

On January 23, a series of major actions were taken by the Chinese government, including a city lockdown and home and centralized quarantines. Some of the measures put in place in Wuhan would not be deemed either societally acceptable or practically feasible in many parts of the world; eg, complete control of movement for months or compulsory isolation in facilities. Other measures put in place at that time (not shown in this figure but widely reported elsewhere) included business closures, school closures, and cancellation of gatherings, which also contributed to substantially lowering social interaction. Those measures have become the core of social distancing interventions taken around the world to control the spread of SARS-CoV-2.

When all those measures were taken collectively in Wuhan, the R_t of the epidemic declined to below 1 within weeks. When an R_t decreases below 1 for a given disease in a given place, disease spread slows and the epidemic has the potential to be controlled in that area.

Figure 2 illustrates what the goal must be now around the world. Until a safe and effective vaccine is developed and globally disseminated, countries need to use some combination of social distancing measures to work to bring their Rt below 1. Hopefully, countries will find strategies to implement social distancing in ways that allow economies to come back and society to resume some normalcy. Given the severe economic and societal consequences of these strategies, continued efforts should be made to study the need for and effectiveness of social distancing measures as they are put in place and relaxed in the time ahead. Beyond the larger measures of business and school closures and cancellation of gatherings, individual actions to keep physical distances of at least 6 feet, wear cloth masks in public, and telecommute to work will help reduce the R_t. Absent any social distancing at all, SARS-CoV-2 would likely revert to its pattern of spread as it was back in early January, with an R_t in the 2 to 4 range and doubling in size every 5 days, until a substantial portion of the population develops immunity through infection and recovery, or through vaccination.

The US Centers for Disease Control and Prevention (CDC) should regularly report on the R_t for the US and for each of the 50 states so that political and public health leaders can gauge how well the combined organizational and individual social distancing measures in place around the country are working to diminish transmission of this virus. The CDC should then communicate this transparently to the public to increase public buy-in and understanding of the actions being taken to slow the spread of COVID-19. 

* Professor and Director of Johns Hopkins Center for Health Security (tinglesby@jhu.edu).

This viral Angela Merkel clip explains

the risks of loosening social distancing too fast

Jag Bhalla

Apr 18, 2020

Germany doesn’t have much “wiggle room” in its hospital capacity. The US has even less.

When you have a huge hole where your nation’s leadership should be, it is wise to borrow the best of other people’s leaders. They can’t make America’s big decisions, but they can fill in some of the gaps.

In the Covid-19 pandemic, we can take comfort in their competence and use their wisdom to guide us about what we each should do.

Right now, the United States and many other nations are considering easing social distancing and other restrictions if and when their new coronavirus cases and hospitalizations become flat or start to fall. And German Chancellor Angela Merkel (who happens to have scientific chops) has an important lesson that we should all listen to.

On Wednesday, she laid out important logic about the coronavirus pandemic that hasn’t been communicated clearly enough here in the US. In simple and clear terms, she explains why Germany doesn’t have much “wiggle room” in its hospital capacity. Because of this, any lifting of its lockdown, like allowing some shops to open next week, will remain “on thin ice.”

Merkel’s explanation, which went viral, is centered on the metric called R0, or basic reproduction number. It represents the number of people a sick person will infect on average in a group that’s susceptible to the disease (meaning they don’t already have immunity).

She says that if Germany’s R0 were to shift from a flat rate of 1.0 to 1.1, the nation’s hospitals would be crushed by October, without sufficient resources to care for all of the severely ill Covid-19 patients. If the R0 goes up to 1.2, that overload hits in July. And so on.

Covid’s current global average R0 is 2-2.5, but Germany has done a good enough job of managing its outbreak to get its reported estimated R0 down to 0.7 as of April 17. That’s low enough for Merkel to sanction “a tentative easing of restriction.”

Germany is not out of the woods, however. Marieke Degen, the deputy spokesperson of Germany’s Robert Koch Institute, told Vox’s Alex Ward that it’s “very important to stress that Germany is still at the beginning of the epidemic” and that more and more elderly people in the country are getting sick.

America, for many reasons, has even less wiggle room than Germany. Germany has eight hospital beds per capita compared to America’s 2.7 beds. In ICU beds, Germany has 8.3 per capita while America has 6.6.

It is also testing for coronavirus at twice the US rate (21 vs 9.8 tests per 1,000 people). Without robust testing, you can’t keep good tabs on R0 or the related Rt — and you can end up flying blind, risking health system overload and avoidable deaths.

Covid-19 spreads in an exponential way, and it’s worth emphasizing exponential growth’s dynamics. Tiny shifts in risk grow very quickly, leading to deadly results, as this useful tweet thread shows:

The small choices we each make about risky behaviors are like playing Russian roulette, but with a machine gun. You may have thought that if you’re not in a high-risk group (like older adults), and the case fatality rate is around 1 percent, then the threat isn’t so great. Surely we can loosen restrictions?

But that’s like being locked in a room with 100 people, where your collective behavior determines how many bullets are live in the machine gun that’s about to strafe all of you. You might not die, but others surely will. 

Covid-19 is already the leading cause of death in many areas, including New York state, Louisiana, and Washington, DC. Do you want to add ammunition to its arsenal?

 R0:

How scientists quantify the intensity of

an outbreak like coronavirus

and its pandemic potential

Joseph Eisenberg*

February 12, 2020

If you saw the 2011 movie “Contagion,” about a worldwide pandemic of a new virus, then you've heard the term “R0.”

Pronounced “R naught,” this isn't just jargon made up in Hollywood. It represents an important concept in epidemiology and is a crucial part of public health planning during an outbreak, like the current coronavirus pandemic that's spread globally since it was first identified in China.

Scientists use R0 – the reproduction number – to describe the intensity of an infectious disease outbreak. R0 estimates have been an important part of characterizing pandemics or large publicized outbreaks, including the 2003 SARS pandemic, the 2009 H1N1 influenza pandemic and the 2014 Ebola epidemic in West Africa. It's something epidemiologists are racing to nail down about SARS-CoV-2, the virus that causes COVID-19.

How much will a disease spread?

The formal definition of a disease's R0 is the number of cases, on average, an infected person will cause during their infectious period.

The term is used in two different ways.

The basic reproduction number represents the maximum epidemic potential of a pathogen. It describes what would happen if an infectious person were to enter a fully susceptible community, and therefore is an estimate based on an idealized scenario.

The effective reproduction number depends on the population's current susceptibility. This measure of transmission potential is likely lower than the basic reproduction number, based on factors like whether some of the people are vaccinated against the disease, or whether some people have immunity due to prior exposure with the pathogen. Therefore, the effective R0 changes over time and is an estimate based on a more realistic situation within the population.

It's important to realize that both the basic and effective R0 are situation-dependent. It's affected by the properties of the pathogen, such as how infectious it is. It's affected by the host population – for instance, how susceptible people are due to nutritional status or other illnesses that may compromise one's immune system. And it's affected by the environment, including things like demographics, socioeconomic and climatic factors.

For example, R0 for measles ranges from 12 to 18, depending on factors like population density and life expectancy. This is a large R0, mainly because the measles virus is highly infectious.

On the other hand, the influenza virus is less infectious, with its R0 ranging from 0.9 to 2.1. Influenza, therefore, does not cause the same explosive outbreaks as measles, but it persists due to its ability to mutate and evade the human immune system.

What makes R0 useful in public health?

Demographer Alfred Lotka proposed the reproduction number in the 1920s, as a measure of the rate of reproduction in a given population.

In the 1950s, epidemiologist George MacDonald suggested using it to describe the transmission potential of malaria. He proposed that, if R0 is less than 1, the disease will die out in a population, because on average an infectious person will transmit to fewer than one other susceptible person. On the other hand, if R0 is greater than 1, the disease will spread.

How many others will each sick person infect?

The reproduction number, R0 for short, describes how many additional cases of a disease each infected person will cause during their infectious period. The numbers are a range, because they depend on a variety of factors that vary from situation to situation.

When public health agencies are figuring out how to deal with an outbreak, they are trying to bring R0 down to less than 1. This is tough for diseases like measles that have a high R0. It is especially challenging for measles in densely populated regions like India and China, where R0 is higher, compared to places where people are more spread out.

For the SARS pandemic in 2003, scientists estimated the original R0 to be around 2.75. A month or two later, the effective R0 dropped below 1, thanks to the tremendous effort that went into intervention strategies, including isolation and quarantine activities.

However, the pandemic continued. While on average, an infectious person transmitted to fewer than one susceptible individual, occasionally one person transmitted to tens or even hundreds of other cases. This phenomenon is called super spreading. Officials documented super spreader events a number of times during the SARS epidemic in Singapore, Hong Kong and Beijing.

R0 for coronavirus SARS-CoV-2

A number of groups have estimated R0 for this new coronavirus. The Imperial College group has estimated R0 to be somewhere between 1.5 and 3.5. Most modeling simulations that project future cases are using R0s in that range.

These differences are not surprising; there's uncertainty about many of the factors that go into estimating R0, such as in estimating the number of cases, especially early on in an outbreak.

Based on these current estimates, projections of the future number of cases of coronavirus are fraught with high levels of uncertainty and will likely be somewhat inaccurate.

The difficulties arise for a number of reasons.

First, the basic properties of this viral pathogen – like the infectious period – are as yet unknown.

Second, researchers don't know how many mild cases or infections that don't result in symptoms have been missed by surveillance but nevertheless are spreading the disease.

Third, the majority of people who come down with this new coronavirus do recover, and are likely then immune to coming down with it again. It's unclear how the changing susceptibility of the population will affect the future spread of infection. As the virus moves into new regions and communities, it encounters people with varying health conditions that affect their susceptibility to disease, as well as different social structures, both of which affect its transmissibility.

Finally, and likely the most important reason, no one knows the future impacts of current disease control measures. Epidemiologists' current estimates of R0 say nothing about how measures such as travel restrictions, social distancing and self-quarantine efforts will influence the virus's continued spread. 

* Professor and Chair of Epidemiology