From One Case to 30,000


How the virus exponentially expands, and the only way to slow it down.

story Kathryn Dreger, M.D.

(Editor’s note:  This is the second letter sent by internal medicine physician Kathryn Dreger to her patients in Arlington, Virginia. Some of the statistics referenced may be out of date by the time you read this, but the precautionary advice and exponential growth explanation are, we believe, of essential importance for everyone to understand.)

I am sure many people are growing tired of this pandemic, tired of the isolation. From wearing masks to facing shortages, from working at home to missing major events, many of us are asking a very simple question, “When will all this end?”

So I want to provide an update on the progress we are making with COVID-19. I know the news is full of information, but I thought it might be helpful to explain the curves we hear so much about on the news. We see them rising. We long to see them falling. At the very least, we’d like to see them squashed, flattened like gum under our shoe. But do we all actually know what an exponential curve is? In order for me explain how we are going to get out from under this pandemic, I must first explain how these curves work.

So, let’s imagine we take down an old checkerboard from the shelf. If we put $1 on the first square and agree to double the amount every time we move to the next square, how long will it take before we have to put down $100? How about $1,000?

The answer is surprising, and it explains why controlling the COVID-19 pandemic seems to be constantly beyond our reach.

Without social isolation and quarantine, COVID-19 cases double about every week. Let’s see how this works by putting $1 on the first square of the checkerboard and seven days later, we’ll move to the next square and put twice as much, or $2 down. By the end of the first row, seven weeks and seven squares have passed, and we’d have to put down $128. It took us nearly two months to go from $1 to $100.

If we imagine each dollar is a person with COVID-19, we can see that it takes about two months for one case to spread to over 100 people. But, in just one more month, the same doubling effect becomes dramatic. The number of cases from just one person rises above 1,000, and it soars to over 30,000 by the end of the fourth month. If a country goes six months without social distancing measures, one infection would lead to over 8 million cases. That’s exponential growth.

Fighting this growth, controlling the spread of the virus from human to human, is one of three prongs of attack in the COVID-19 pandemic.

In an ideal world, every person with COVID-19 would promptly be tested and interviewed in detail by a public health official to figure out who they have seen and where they have been while they were contagious. Those contacts would be traced down, tested if they had symptoms or quarantined for 14 days. This mundane tricky task, called contact tracing, is and always will be the key to controlling a pandemic. It takes a lot of effort.

The easiest time to do contact tracing and control the growth of the virus is when a town has very few cases, like less than one hundred and only one death. But, it’s hard to jump to attention when the numbers are low. One death, while sad, is not terrifying. In every state, in every country, the first few cases seem so insignificant, so trivial. It’s so easy to reassure ourselves, to look away and live our lives. It’s so easy to forget that the virus is alive – and growing. It doubles, and doubles and doubles again. By the time the numbers get our attention, the virus is beyond our control.

And, once COVID-19 gets hold, once the cases soar into the thousands, the number of ill people overwhelms the ability of public health personnel to do contact tracing. The safest solution is to just stop all contact. Shelter in place. Stay away from each other. Wait for the numbers to go down. That’s where we are now.

We are trying as hard as we can not to move to the next square, not to double the growth of the virus. We are staying home, washing our hands and cleaning surfaces. We are working remotely, and when we go out, we are practicing social distancing and wearing masks.

Yes, it’s drastic. Yes, it’s clunky, but here’s the thing I want you all to know. It’s working. I mentioned before that unchecked, COVID-19 cases double every seven days. On April 11, we had 500,000 cases. We reached a million cases on April 29. Our doubling time is nearly three weeks. Yes, the numbers are huge, and the death toll is heartbreaking. But, the aggravating, tiresome, frightening activity of staying home is working.

Well done! Now, let’s look forward. When can we ease self-isolation? Public health officials are our heroes here. They know what needs to happen next.

As long as the number of positive tests is going up, they know that we are still moving from square to square, more cases are coming in.

Only when the cases start going down do we know we have turned the tide and the virus is losing.

It takes at least a week for each infected person to be diagnosed and counted. I don’t think we can escape this lag even with excellent and rapid testing because it takes about five to seven days for people to develop symptoms, and we think the tests might be negative when a person is in the first asymptomatic days of a real infection.

We have to remember that on any given day, we are getting the results of the infections that were caught at least seven days before. During those seven days, the virus has continued to spread, and without social distancing, has continued to double. The numbers we see each day could be much higher. They just have yet to be counted.

Because of this lag in the system, the numbers have to be going down for two weeks to really know that any drop we see is not a fluke. That’s what we are all waiting for. And, this is really important, the tighter we are about self-isolation, the sooner that will happen.

Two week decline before re-opening.

Different regions of the country will see this pattern at different times, depending on how many patients they had when they started isolating (where they were on the checkerboard when they started) and how tightly they are controlling the spread of the virus. So, we should see different states recommend lifting restrictions at different times. That’s fine as long as the public health officials have proven a two-week decline in cases.

Can you please keep track of where and when you go out? That way, if you do get sick, you can help the public health officials find the people you were in contact with.

When restrictions are eventually lifted, we will probably have to wear a mask all the time. When we go back to work, we will also need to keep ourselves six feet apart. How will you have to change your life to make that happen?

You can start on this project now.

Please think about your workplace. Ask your colleagues, bosses or employees how you can make this work. Can you move desks? Can you have two work teams who come in for two weeks at a time and alternate? If so, who would those people be? How can you divide the work?

These are practical but complicated questions. They will take time and each company will have a different answer. We shouldn’t wait for these restrictions to ease before we tackle these problems. The sooner we all start considering these questions, the better prepared and the safer we will be when we go back to work.


Our second prong of attack against COVID-19 focuses on treatment.

We are learning how to treat this disease. We all know we need a medication to treat this infection. If we had that, we could save people, reverse their disease, and avoid the ventilators. The death toll would drop and COVID-19 would be less dangerous. I am sure you have heard of many drugs in the press, but they are all ideas, hopes, and dreams until we prove that they work. We have a motto in medicine, “First Do No Harm,” and some of these medicines can make people sicker. Doctors from all over the world are learning, sharing their data with each other, answering questions and building the scientific knowledge of COVID 19.

Virginia Hospital Center is also currently enrolling patients in two trials.

According to the American Medical Association, there are currently 291 clinical trials underway specifically aimed at COVID-19. While this virus is fast, the speed of discovery, of science in its purest form, is astounding. I am so grateful and proud of my colleagues for their diligent, thoughtful, courageous and hard work. We are making progress, and we will have more facts soon.


Our third prong of attack against COVID-19 is to develop a system of long-term virus control.

As I write this, over 3 million people on the planet have tested positive for COVID-19. Eradicating this infection would be lovely, but I think it might be here to stay. We must learn how to control the virus over the long-term.

The first, and most obvious way, is a vaccine. There are at least 107 different programs all over the world actively working on getting a vaccine. They are all approaching the problem slightly differently, which is great. The more avenues we try at once, the more likely we are to succeed.

Importance of testing and contact tracing

Until then, we must become excellent at testing and contact tracing. Once the cases decrease and we resume more normal lives, the virus will likely sneak out again.

We actually have excellent testing now. In the USA, we have tested over six million people. I believe the technology will flourish in the months to come. It is already transforming care during the pandemic and will continue to do so. But, all over America, we must hire more public health professionals to do the difficult and critical work of contact tracing. If we have excellent contact tracing systems in place, we can capture future outbreaks early, quarantine aggressively and allow those not affected to carry on with their lives. Please ask your elected officials how they are increasing the manpower for public health.

We must all be careful when we see the numbers rise again. We must not reassure ourselves or look away and live our lives. We must remember that the virus is alive – and growing.

This is particularly important if we focus too much on the number of people who have died. Please let me explain. People who die from COVID-19 do so about three to four weeks after they were infected. In other words, the people who died today were infected about a month ago. During that time the virus can continue to spread. If social distancing is not in place at all, the numbers will have been doubling each week. Following the death rate alone will make us far too slow to jump to attention. The exponential curve will have restarted, and we will have to do all of this again.

Small town strategy

That’s why what happens in small towns all over the country is particularly important. Many have only a few cases, are sitting in the first few squares of the checkerboard. We might feel like most of our efforts should go to the hardest hit areas, but now that we understand exponential curves, we know that we can save more lives by keeping those small towns stable on the first few squares of the board. They might even be able to prevent closing down completely or for very long if they do quick effective testing and excellent contact tracing. If you have family or friends in these towns, please reach out to them and let them know. By intervening early, they are in the position to save the most lives.

Antibody testing

We are also learning how many people have been infected with COVID-19. We can’t make up for the missed tests in February and March, but we will learn how many people have had the disease with antibody testing.

According to experts, these tests seem reliable, but there is so much we don’t know. Antibody testing is not everything. I cannot state this more plainly: We have no proof that having an antibody to COVID-19 means you cannot get the infection again. Until we have that proof, imagining that antibody testing will be a ticket to return to work is simply wishful thinking. Science needs to prove that dream true before we make any plans on the results.

People with antibodies to COVID-19 must still follow social distancing precautions and shelter in place. Until we know otherwise, please don’t imagine that having an antibody to COVID-19 means you are safe.

Finally, saving this many lives comes at a huge financial cost. I am not talking about the medical care, but the jobs lost due to the dramatic change in our society. We owe it to each other to figure out how we can help struggling businesses or transform our own for a new reality. This virus will not last forever, but it will be a force in all our lives for months more.

So, while spring slides into summer and we long for this to be over, please know we are gaining on all three fronts. We are flattening the curve with hand washing, social distancing, face masks and timely testing. We are learning how best to treat the sickest patients both on the hospital wards and in the ICU. Scientists are working hard on a vaccine and how best to use antibody testing moving forward.

Unfortunately, science cannot be rushed. It makes us prove what we believe. It forces us to search for harm we might create. It is humanity’s guard against the traps of being human, it stops us from rushing to judgment, from jumping to conclusions. We must all be patient and allow this work to be done properly.

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