“Perfect numbers like perfect men are very rare.” Rene Descartes
“Prediction is very difficult, especially if it's about the future.” Niels Bohr
Everyone knows that just about every activity (and even inactivity) carries some degree of risk. We go about our daily lives calculating—mostly unconsciously, thank goodness—what’s safe or risky. And if you’re like me, you’re dumbfounded by people who seem to thrive on taking big risks, such as climbing Mount Everest or participating in extreme sports.
In the era of the rapidly expanding COVID-19 pandemic, many of the burning questions about risks aren’t fully answered, for example: 1) what’s my risk of getting infected with the coronavirus that causes COVID-19; 2) if I get infected, what’s my risk of dying?; and 3) are the measures to “flatten the curve” (social distancing, sheltering in place, etc.) working, and when can I get out of the house and start my life again?
Math in the Time of COVID-19. First, an anecdote from my remote past about math. I vividly remember in an interview at the University of Chicago Medical School when the dean expressed this opinion, “. . . the best preparation for becoming a doctor is a math major.” Math wasn’t one of my strong suits, so that school was out. But I’ve often wondered since whether he was prescient about the yet to be born fields of medical informatics and artificial intelligence or was he referring to the enormous importance of mathematical models in steering public health decisions or in advising individual patients about risks of treatments or the prognoses of various illnesses?
As you’re likely aware, for people who believe science should guide all recommendations about health policies, the evidence generated from mathematical models has become a major epidemiological tool. The math underpinning these models involves very sophisticated statistical analyses that are way beyond my ability to comprehend. But weighed in the balance are factors that we all can understand, for example, how contagious is SARS-CoV-2 (expressed as the basic reproduction number or R0), how lethal is the infection (the case fatality rate or CFR), and how many people are at risk of infection (that is, they aren’t immune)?
The good news is that many brilliant minds have developed these mathematical models. The bad, but perhaps not surprising, news is that they don’t always agree with one another. As hard as it may be to believe, we still don’t know a lot about COVID-19; we are still on a steep learning curve. Thus public health authorities must sort through different, sometimes contradictory, projections and rely on the best, but imperfect, evidence.
In my opinion, two fundamental problems underlie prediction models for COVID-19. First, for many calculations it is critically important to know how many people have been infected—a still elusive number in the United States because testing for the virus was hobbled by a faulty rollout of testing capability. And on a related note it’s also important to know how many infected people don’t develop symptoms and yet can transmit SARS-CoV-2 surreptitiously to others. The second problem, which is unfortunately insurmountable: nobody has a prediction model that can predict the unpredictable (the unknowable unknowns). (If this weren’t the case, meteorologists would always nail the weather forecast and investors in the stock market would always do as well as Bernie Madoff did but without cheating.)
What’s your risk of getting infected? As you would imagine, the answer to this question depends on many variables, such as, where you live, how many infections have already hit your country or community, and how often you come in contact with infected people whether or not they have symptoms of COVID-19.
The initial estimates of the contagiousness of SARS-CoV-2, derived from several mathematical models, suggested it has an R0 value between 1.4-5.7. By comparison to other human coronaviruses and influenza viruses, all of which are also transmitted primarily by airborne droplets, SARS-CoV-2 seemed to be in the same ballpark. (Fortunately, this is nowhere near the contagiousness of measles virus, R0 12-18, which is also spread by respiratory droplets.)
Some experts believe the R0 of SARS-CoV-2 is higher than initially thought. And if you live in America where the number of cases mushroomed from fewer than 100 in early March to more than 1 million by the end of April, it doesn’t take a rocket scientist (or mathematical modeler) to recognize that this a very contagious virus, and that, unless a vaccine comes along, many of us are likely to be infected sooner or later.
If I get infected, what’s my risk of dying? Calculating the CFR of COVID-19 has been seriously hampered by the lack of laboratory testing for SARS-CoV-2. If only those who are symptomatic are tested, the CFR will be artificially high because we would be capturing only the classic “tip of the iceberg.” And if we include those with asymptomatic infections, which some studies suggest is as high as 50% of infections, the CFR will decrease as the denominator increases. That said, on April 21, Johns Hopkins University Coronavirus Resource Center estimated the CFR of COVID-19 at 1.38%, but 0.68% if asymptomatic infections are included.
While the CFR of COVID-19 is somewhat lower than that of the notorious 1918-1919 flu pandemic (CFR>2.5%) and orders of magnitude lower than those of the other coronavirus pandemics (SARS, CFR 11%; MERS, CFR 43%), as with many aspects of COVID-19 we’re in the early learning stages about the severity of COVID-19. Although testing for SARS-CoV-2 is ramping up in the United States, it is still woefully inadequate. But once antibody testing is widely available for surveying populations of people (called serological surveys or serosurveys), we will have a much better idea of the true CFR of COVID-19. We need to wait a little longer for this answer.
Risk factors for severe disease. It is perhaps reassuring to know that if the coronavirus that causes COVID-19 catches you, odds are probably less than 50% that you’ll become ill and less than 1% that it’ll kill you. But as you likely know a number of risk factors can worsen your odds considerably. From the very beginning of the pandemic, the elderly and those with chronic medical conditions were found to have an increased risk of severe or fatal COVID-19. People 65 years-of-age or older remain the biggest risk group for fatal infection. In Minnesota, like many states, almost all recent COVID-19-related deaths have occurred in long-term care facilities. News stories about marathon runners and those in prime physical condition who are dying are tragic but, mathematically, they are outliers.
The list of chronic medical conditions that predispose to more severe COVID-19 includes: chronic heart, lung, kidney, or liver disease, diabetes mellitus, severe obesity (body mass index >/40), and conditions associated with compromised immunity, including cancer treatment, bone marrow or organ transplantation, poorly controlled HIV/AIDS, or use of corticosteroids. Members of certain racial and ethnic minorities and the unsheltered homeless are also at increased risk of severe disease. From the beginning of the pandemic, COVID-19 has been known to take a bigger toll in males than females. Whether this is due to gender-related biological factors, such as, hormonal or gene variations, or behavioral differences, such as smoking, is not yet clear.
Flattening the curve or flattening the economy. Whether we like it or not, massive experiments guided by different mathematical models have been going on since the beginning of the COVID-19 pandemic, at international, national, and local levels, all attempting to control the spread of SARS-CoV-2. Sociopolitical and cultural forces have profoundly influenced strategies to defeat this tiny mortal enemy.
It’s too early to tell what approaches have worked best. Not enough dust has settled yet. But one thing’s for sure, mathematical considerations will continue to drive important decisions, such as: Is 6 feet sufficient social distance to work?; How large a gathering is too large?; Have we reached herd (community) immunity?; When can we return to work, school, and our favorite restaurants and entertainment venues? Again, we need to wait a little longer for these answers.
It’s reassuring to know that many talented scientists around the world are working together on answering these and other questions about what containment strategies have worked best. According to a paper in the April 27 issue of Nature, whole teams of mathematic modelers are involved at the London School of Hygiene and Tropical Medicine and at the University of Oxford. So far it appears that countries that had policies for aggressive early diagnosis, case finding, and social distancing have fared best.
No one can predict exactly when COVID-19 will be conquered, but based on the outcomes of many earlier battles with other microbial enemies, it will be defeated. Results of early clinical trials suggest that medical therapies soon will be found, and a vaccine seems possible even within a year’s time. Even though the numbers of infections and deaths worldwide are piling up, as Irving Berlin said "When I'm worried and I can't sleep, I count my blessings instead of sheep." We’ve all witnessed countless acts of kindness—these numbers are also going up.
Finally, on top of a large dose of patience, I recommend a huge measure of common sense. For example, take this sign by the side of the lake near our home. For some, common sense would dictate that the people in the photo should find another rink.
