Beneath the Surface

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Last week I said that the United States was poised to become the world leader in coronavirus cases very soon. That milestone has now been reached, as our 20,608 deaths have surpassed every other country. That includes China, despite the fact that it is less economically developed, has four times our population, and was first to be hit by what became a pandemic.

However, this week we also had evidence that our steeply rising mortality curve is starting to flatten. Total deaths did increase 142% during the week—that is, they more than doubled—but they had nearly quadrupled the previous week. Deaths are still rising, but the rate of increase declined in almost every state. (The exceptions were Idaho, Missouri and Oregon.)

Nevertheless, the spread of the disease remains alarming. With over 20,000 deaths already, any more weekly doublings would result in astronomical death tolls. Epidemiologists have developed much more sophisticated models for the spread than I can describe here. One of them that has gotten a lot of attention projects that we can hold this year’s ultimate death toll to 60,000. Whether we can do that while quickly putting the country back to work is not as clear.

What have we learned?

What have we learned from experiencing this pandemic so far? Are we drawing the right lessons? In particular, what has President Trump learned? We know that he initially underestimated the problem, and that he continued to treat it dismissively for weeks after being briefed by both intelligence officials and medical experts. We also know that previous administrations—both Republican and Democrat—had developed plans and proposals for dealing with a pandemic, and that this administration chose to ignore them. How much has the President wised up since then?

The first lesson most of us have learned is that a pandemic requires a quick and decisive response, since every week counts. Locating cases and quarantining the infected are crucial.

The second lesson is that a country can slow the transmission of a contagious disease by telling most people to stay home, although that is a crude way of doing it. At the very least that strategy can spread the caseload over a longer time, easing the burden on medical facilities. Hopefully, few states will now experience what New York has just been through.

But then what? How does a country permanently limit the number of people who contract the disease and the number who die from it? The ideal solution is general vaccination, but that appears to be at least a year away. Another possibility is a breakthrough in treatment, to make the disease less life-threatening, but that also appears a number of months off.

Advocates of a quick return to business as usual seem to be relying heavily on “herd immunity,” the idea that once a lot of people have survived the disease and developed immunity, new cases will peter out. We can also use the antibodies in the blood of survivors to treat those who do get sick. But how large would such a “herd” of survivors be? Right now, we have about one death for every 25 confirmed cases. That means that we could get to 60,000 cases with only 1.5 million Americans having contracted the disease, leaving the vast majority of our 330-million population still at risk with no immunity. Of course, the reported numbers of deaths and cases could be wrong. Maybe a lot of deaths have yet to show up, since it is a “lagging indicator,” and some deaths occur at home without being correctly classified. The number of cases could be even more seriously underestimated, since people can have mild symptoms without reporting it as covid-19 at all. But even if the real ratio of deaths to cases is only one in 100, we could have 60,000 deaths from only 6 million cases, still leaving most of the population unprotected.

Most medical experts are dubious about the President’s eagerness to “reopen” the economy. We would be ending the strategy we’ve been relying on to stop the dying, and sending people back into society with no more protection than homemade face masks.

Test, test, test

What the experts do recommend is what should have been done earlier on. Scale up testing to the point where new cases can be quickly identified and selectively quarantined, while other people start to feel safer going about their business. That’s what countries with the most success in halting the epidemic have been doing. In contrast, President Trump’s consistent pattern of over-promising and under-delivering testing is a national embarrassment.

I doubt that the economy can restart with one big rush of people back to work. It’s going to be a while before people are comfortable in crowded workplaces, shopping malls, stadiums, or on buses, subways or airplanes. Given the great variety of workplaces, shopping areas, entertainments and methods of transportation, I suspect we will have a patchwork economy for a time, with some places a lot safer than others. That should make the overall recovery a bit sluggish, especially since the various parts of the economy are interdependent. One business cannot thrive if some other business it depends on cannot operate safely.

Another widespread prediction is that technological means of interacting and producing without face-to-face interaction—automated production, teleconferencing, online shopping, etc.—will get a permanent boost from this experience. But reorganizing along those lines will take time, and it will require some upgrading of the skills of many workers if they are to remain employed.

Instead of a quick return to “normal”, we should expect a painstaking transition to a new normal.

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This has been a week in which hospitals in New York and many other states began to be overwhelmed by the exponential growth of coronavirus cases. When every patient counts and every death is a tragedy, the sheer number of cases is daunting.

Having said that, epidemiologists have to look at rates and growth trends as well as sheer numbers to understand an epidemic, and so do the rest of us. In last week’s post, I used the concept of doubling time to compare mortality trends in different countries, based on data from Our World in Data. The good news this week is that the doubling times in days are increasing a little in most countries, meaning that the rate at which deaths are multiplying is slowing. The bad news is that exponential growth curves are still very steep in many places. Deaths are doubling every four days in the United States and United Kingdom, apparently the fastest growth in the world. The doubling times are five days for Germany, six days for France and Netherlands, seven days for Spain, and ten days for Italy.

To appreciate the implications, if Italy’s deaths would keep doubling every 10 days for the next 30 days, its 15,362 deaths would double three times, increasing by a factor of 8 to 122,896. But if US mortality would keep doubling every 4 days in the same period, its 8,501 deaths would double at least 7 times, increasing by a factor of 128 to 1,088,128. To put that in perspective, 405,000 Americans died fighting World War II. No one knows what the real numbers will be, since no one knows how much and how fast we can bend the growth curve. What is clear is that the United States is poised to become the world leader in coronavirus deaths very soon. How the country that prides itself on the world’s most advanced health care system could accomplish that feat is a topic for another time.

State mortality rates

Within the United States, death rates also provide additional perspective to raw numbers. As of this morning, the ten states with the highest number of deaths are New York, New Jersey, Michigan, Louisiana, Washington, California, Illinois, Massachusetts, Georgia, and Florida, based on data from the Washington Post. Taking into account state size by using deaths per 100,000 population changes the picture somewhat. California’s 289 deaths no longer look so large, and Vermont’s 20 deaths become more significant. California’s rate of less than 1 death per 100,000 drops it down to 30th in death rate, while Vermont’s 3 per 100,000 brings it up to 7th. Illinois, Georgia and Florida also drop out of the top ten, to be replaced by Connecticut, Colorado and the District of Columbia. The number of deaths in a small state may get less attention, but it can have a large proportional impact on the smaller number of medical personnel and hospital beds.

Not only do states differ greatly in total deaths and death rates per 100,000 to date, they are also adding deaths at very different rates. Most of the states with the most deaths—either raw numbers or deaths per 100,000—have also had relatively large percentage increases over the past week. Increases of 300% or more are common—New York’s is 331%—but Michigan and New Jersey have seen increases over 500%. One notable exception is Washington, which has the sixth highest death rate so far, but one of the slower rates of weekly growth, 67%. The virus hit Washington first, but stay-at-home measures seem to be working. California has both a low rate of death and a below-average rate of weekly increase, having been the first state to issue a stay-at-home order.

Meanwhile, other states have had relatively low numbers and rates of death so far, but now have above-average rates of growth. Tennessee’s mortality rate is less than 1 per 100,000, but its deaths increased from 7 to 50 in a week, an increase of 614%. Other states that experienced significant jumps from low beginnings were Alabama, Kentucky and Maryland.

Given the potential for exponential growth to change the situation with dizzying speed, current low numbers are no excuse for complacency, anywhere in the country.

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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?

Exponential growth

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.

Mortality trends

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.

Safe places?

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.