If you’ve been paying attention to the reporting about the spread of the novel coronavirus in the United States, you have probably heard about how experts hope to “flatten the curve.” The idea, in short, is that by slowing the rate of transmission of the virus, we slow the number of people who need treatment for it. By slowing the number who need treatment, we make it easier for hospitals to handle the number of cases that are arriving in any given day or week.

Think of it this way. Let’s say that 1.2 million people are eventually infected with the virus, a relatively low estimate given the current rate of spread. The difference between those 1.2 million people being infected over the course of a year and over the course of two months is 500,000 people monthly: 100,000 people a month being infected in the first case and 600,000 a month in the second. Since experts estimate that 10 to 20 percent of those who contract the virus will need hospital care, that’s the difference between 10,000 and 60,000 people heading to the hospital in a given period.

That’s important not only for the treatment of patients ill with covid-19, the disease caused by the virus, but for everyone else who needs hospital care. If you get in a car accident, your survivability may be a function of whether every intensive care unit in the closest hospital is already occupied by someone ill with covid-19.

Over the past several weeks, the number of coronavirus cases recorded in the United States has begun to escalate quickly. Since the beginning of the week, the number of cases has more than doubled. In recent days, the number of recorded cases has grown at nearly 30 percent a day.

The actual number of infections is almost certainly an order of magnitude larger than that. The above data include only confirmed cases, ones which have been identified by official testing. Since that testing hasn’t been broadly deployed, it’s an undercount.

So we don’t really know the current rate of spread. If it is 30 percent nationally, though, that’s a problem, given the estimates of the need for hospitalization and an estimate that about 1 percent of those who contract the virus will die as a result.

Assuming about 1,700 current cases, here’s how constantly daily increases of 10, 20 and 30 percent yield different infection totals over the next 30 days. (In the graphs below, we’re using the low-end, 10 percent estimate for hospitalization rates.)

Breaking out the hospitalizations and deaths alone yields a stark difference.

This is an academic exercise and doesn’t reflect what we might actually expect. You’ll notice on the chart of the actual spread of cases that the daily increase is variable, for example. It does, though, show how dramatic a difference an increase in growth rates can be. If we add 10 percent more cases every day for the next 30 days, 2,700 people will need to go to the hospital. If we add 20 percent more cases a day, that jumps to more than 33,000. If we keep adding new cases at an increase of 30 percent daily, the total by April 11 is 343,000.

That’s particularly problematic because there are currently only about 45,000 intensive care units in the United States. If everyone being hospitalized for covid-19 needs an ICU, all of those beds would be filled by April 4 in the 30-percent-increase scenario.

Growth rate makes all of the difference. You can use this interactive to explore how different growth rates affect infections and hospitalizations under the criteria above.

If you increase the growth rate enough, you’ll reach a point at which the number of people being infected hits a theoretical upper limit imposed by herd immunity. Experts who spoke at a recent panel at University of California at San Francisco estimated that once 40 to 70 percent of the country has contracted coronavirus, enough people would have antibodies for the virus that its spread would be limited in the way that the spread of other illnesses (like the flu or measles) is limited by widespread vaccinations.

At some point, we’ll reach the level of herd immunity, ideally through the introduction of a vaccine to protect people against the novel coronavirus. It would be substantially more catastrophic if, instead, that point was reached within a month because the virus raged across the U.S. without constraint.

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