In my state of North Carolina, Governor Roy Cooper has now issued a statewide stay-at-home order to slow the spread of the coronavirus. Effective March 30 to April 29, the order prohibits gatherings of over ten people, requires people to remain six feet apart, and limits activities outside the home to visits to essential businesses, outside exercise, and assistance to relatives.
One might ask why a state with only four deaths, in contrast to over 600 in the state of New York, is taking such drastic action, with obvious economic implications. Why not wait until the situation is more clearly a crisis? Why not do as President Trump recommends—try to identify “low-risk” counties where life can be allowed to go on as usual?
I think that such objections reflect a misunderstanding of the problem. They underestimate the power of exponential growth to turn a numerically small problem into a major disaster very quickly. We should have learned that lesson by now from observing what happened in Italy (which leads the world in coronavirus deaths) or New York (which leads the states).
The numbers of cases and deaths are changing as I write this. Within a few days, the numbers I cite in this post may well have doubled. Infections and deaths from infectious diseases increase exponentially rather than linearly. They increase not by the same increment every day, but by an increasing increment every day. The greater the number of people already infected, the greater the number of others who can contract it from them, until the virus runs out of people to infect.
At first, the rate of exponential growth can be extremely high, with infections doubling every day or two. This is especially true for a new virus, for several reasons. No one has immunity yet; there isn’t widespread testing to identify and quarantine the infected; and countermeasures like physical distancing have not yet been adopted. Eventually, the rate of spread will slow because all these things change. Many people have recovered from the disease and are now immune; testing becomes more routine; and people take more precautions.
The best way to grasp the implications of exponential growth is to consider the time it takes infections to double. If they double every six days, they will double five times in a month, which is an increase by a factor of 32. A hundred cases would grow to 3,200 cases in a month. But if infections double every two days, which is quite common in the initial stage of the process, that is fifteen doublings in a months, or an increase by a factor of 32,768. At that rate the initial hundred cases grows into 3,276,800!
Slowing the growth rate by increasing the doubling time by even a day or two can make the difference between a serious problem and a catastrophe. Graphically, it is known as bending or flattening the curve. That spreads the cases out over a longer time, so that health care facilities are not overwhelmed. After all, most hospitalizations are resolved either by recovery (hopefully) or death (sadly) within a few days or weeks. In addition, the longer people can put off getting sick, the greater the possibility of a better treatment or even a vaccine.
Now for some real numbers. I’ve taken these mortality numbers from Our World in Data for countries, and The Washington Post for states. Again I caution that they are changing rapidly.
Coronavirus deaths for the world as a whole are currently doubling every six days. Doubling times are shorter for the most affected countries—three days for the United States and Germany, four days for Spain, France, United Kingdom and Netherlands. A glimmer of hope is that Italy, the country with the most deaths so far, has now increased its doubling time to seven days. China, where the virus apparently originated, has flattened its curve even more, although the official numbers may not be entirely reliable.
The United States is now the leading country in known infections. Its rapid growth in deaths will probably make it the mortality leader as well in the near future. The US response has been scandalously slow, especially in the area of testing. Our failure to test and quarantine suspected cases has made a general lockdown more essential.
In the states with the most rapid growth in infections, such as New York, New Jersey, Michigan and Louisiana, deaths are doubling every two days. On the other hand, the state with the first big surge in mortality—Washington—has flattened its curve somewhat and is now doubling only every six days. More states need to move in that direction.
The most important point is that a relatively low caseload at the moment is no reason to carry on business as usual. What matters is the rate of growth, and states like North Carolina need to take preventive measures now to keep it as low as possible.
Nor can we assume that the rural counties or states with fewer cases so far are not at risk. If the distribution of mortality turns out to resemble that of flu, then states like Nebraska and the Dakotas will eventually exceed more urbanized states in death rates, perhaps because of more limited access to hospital care.
Governors like Roy Cooper are doing the right thing by telling people to stay home throughout the state, not just in areas initially affected, like Charlotte and Raleigh-Durham. More complacent governors ought to pay attention.