Every day, it seems, we’re buried in a new avalanche of numbers, data and graphs related to the COVID-19 pandemic. Every county, state and country is grappling with interpreting and finding the best response to this data, and on a personal level, so is each one of us. To make matters worse, it’s all too easy to conflate the different kinds of risks we face in everyday life. No doubt you’ve heard the argument: “We have to open. There’s risk in everything — I could be hit by a bus while crossing the street.”
For the numerically inclined, the challenge is how to calculate the magnitude of personal risk in order to better inform our personal decisions. This month’s Insights puzzle, then, is an effort to find the best sources of useful pandemic data, make sense of the numbers, find best practices on parsing the data, and reach reasonable conclusions while spotting misinformation, false conclusions and specious claims. I invite Quanta readers to contribute their own insights on the best ways to do this. Unlike some puzzles, this one does not involve especially difficult mathematical techniques. What’s harder is that, as with scientific research, we have to reason with limited knowledge in the face of uncertainty, find reliable sources, exercise a healthy skepticism of the data and make reasonable, principled extrapolations for specific information we may not have. There are no perfect answers, but it is critically important not to be too wrong.
First let’s look at the big picture.
Puzzle 1: Threading the Needle
Our first puzzle is simple to state: Is the actual number of people infected per day by the novel coronavirus in the U.S. during this current period (late July to early August) greater, less than or about equal to the number in the initial peak in the middle of April 2020? If it’s higher or lower, to what extent? (Use sources that are recognized as reliable, such as Johns Hopkins University, The New York Times, Oxford University or the CDC.)
Note that the peak of newly confirmed cases as shown by the seven-day average in the second week of April was around 31,000 every day, while the number during the past week is about twice that — around 60,000. On the other hand, the peak number of reported deaths by COVID-19 per day based on the seven-day moving average was over 2,200 in mid-April, but it’s about half that — around 1,200 — in early August. There is no evidence that the lethality of the virus itself has changed, so this disparity must have other explanations. One reason for these differences is that the actual number of people infected during both periods was far higher than the number of confirmed cases, which only count the number of people who have tested positive or were clinically diagnosed. The CDC director estimated that the actual number of cases may be 10 times greater than the number of confirmed cases and this ratio may not have been the same for the two periods. The steady increase in testing since the early days of the pandemic is relevant here. The ratio of the number of tests to the total number of confirmed cases for the entire U.S. was only about 5-to-1 in mid-April, and is now about 12.5-to-1, so we are certainly finding more of the milder infections.
Answering the above question as accurately as possible requires understanding the complex interaction between confirmed cases, reported deaths and testing numbers, and using this to get to the bottom of how many people the virus has really infected. The number of people who have actually died is not reflected in the reported death numbers either, but the discrepancy is smaller — the best studies we have conclude that deaths caused by COVID-19 are probably underestimated by 30-40%. Several additional complications need to be factored in, such as the possibility that a larger proportion of the April deaths may have taken place as a result of nursing home infections, which we may have gotten better at avoiding. Also, the treatment of seriously ill patients is almost certainly getting better as physicians learn more about effective care.
Of course, to get an accurate answer to the above question is extremely difficult, and even sophisticated published models may not agree. But what I’d like you to do is ponder this question, pick the factors that you think are most important, and give them an approximate weighting based on the best data you can find. Getting at the actual number of infections is a far more complex task than simply using reported rates that are not completely accurate representations of the underlying reality. All we can do is make the best, most reasonable estimates we can.
Let’s now turn to the assessment of personal risk. We have looked at this before in a whimsical Insights puzzle in which we discussed the unit of personal risk, the micromort, invented by the Stanford scientist Ronald Howard, a pioneer of risk analysis. The micromort is a one-in-a-million chance of death and is approximately the risk of unnatural death that a person living in the U.S. assumes every single day.
Here are approximate risk levels associated with some activities and procedures. The numbers indicate risk levels that these activities would add to the daily 1 micromort baseline risk. Note that the numbers are approximate and may vary by a few percentage points between different sources.
Skiing: ~1 micromort
Skydiving: 6-7 micromorts/jump (2010-2019)
Running a marathon: ~9 micromorts
Giving birth: ~175 micromorts
Getting a colonoscopy: ~300 micromorts
Cardiac catheterization: ~1,400 micromorts
Ascending Matterhorn: ~2,800 micromorts
Ascending Everest: ~39,000 micromorts
If you develop the symptoms of COVID-19, your risk of death on average is about 10,000 micromorts (1%), but it increases with age and if you are over 80 it rises to 150,000 to 300,000 micromorts.
This sharp increase based on age illustrates the fact that when you determine risk based on statistics, it helps to use as much local and specific information as possible. Thus, the average risk of driving might be a certain amount, but if you knew it was on a dangerous mountain road, the assumed risk is higher, and if it was snowing and the driver had imbibed alcohol the risk is even greater. Similarly, in the case of the coronavirus, if you know your own personal risk and the rate of positive cases in your immediate neighborhood, it’s better to use those numbers rather than the average rate in your city or state or country. You can calculate your personal risk of death if infected with the novel coronavirus, based on your age and pre-existing health conditions, at one of the many COVID risk calculators.
With that in mind, let’s try to estimate the daily risk the pandemic has added to our lives.
Puzzle 2: Establishing a Risk Baseline
Imagine that you live in a state with a population of 1 million that had 1,000 deaths due to COVID-19 over a period of 100 days during this pandemic. Your habits and behavior during this period lead you to believe that your risk is average. What was your average daily risk in micromorts?
You can extrapolate this to your own situation by using local numbers and adjusting your relative risk up or down depending on your age, state of health and activity level.
OK, you’ve followed the shelter-at-home orders for four months, you’ve been careful and safe, and the numbers in your state are getting better. Like everyone else, you want to open up — get back to a semblance of normal life. You plan to attend a backyard party. Even if there is distancing and mask wearing (which should be a must), you know it is going to entail some additional risk. People tend to relax their own safety standards as they go with the social flow. Someone — a close talker — may interact with you at less of a distance than you’re comfortable with. The birthday boy may lower his mask and blow out the candles, subjecting the cake and the people close by to the entire volume of air in his lungs. The spread of COVID-19 in some states has been linked to outdoor summer backyard parties. Please be safe, follow recommended guidelines, always remain vigilant and take all the recommended precautions!
Puzzle 3: How Safe Is Your Backyard Party?
Let’s say the numbers in your state are such that 1 in 500 people tested at random are positive for COVID-19 (this is the active infection rate). You go to a backyard party with 20 other guests. You interact closely with five people, moderately with another five and distantly with the remaining 10. The interactions are such that your chance of catching the virus from any person in the first group is 1 in 10 if that person is infected; for the second group the chance of infection is 1 in 30, and for the third group it’s 1 in 50. What’s your risk of infection? How many micromorts does that translate to?
The reported rates of infection in one study are about 13% for typical interactions at a distance of less than one meter and 3% for a distance of more than one meter. A face mask reduces these numbers by a factor of 5. As before, you can modify the details of the above to suit your situation and party. The numbers for random testing in your own area may not be available — but you can usually find the positive test rate. Try to reasonably extrapolate from this to get the active infection rate — it’s related to the estimation we made in Puzzle 1. Note that the numbers provided are similar to those in states that have successfully flattened the curve. (If the numbers in your state are rising or much higher than the above example, you probably should not be attending a backyard party.)
The risk calculated above, however, needs to be modified by what we now know about the spread of the novel coronavirus. Recent research shows that as few as 10% of infected people might be responsible for 80% of the spread of the virus. Since the period in which people are presymptomatic and infectious only lasts for two to three days, we can apply this information to backyard parties.
Puzzle 4: The Superspreader Factor
Assume that your average risk of infection at a single backyard party is what you calculated in Puzzle 3. However, factor in that 10% of parties account for 80% of infections. How does that affect your risk of infection from attending one backyard party? What is the risk of catching an infection if you are at a party attended by an infected person? (Note that the chances of catching an infection from specific groups in the party, given in Puzzle 3, are no longer relevant for this problem.)
I hope these examples are helpful as you assess the COVID-19 data and your personal level of risk. Keep in mind that even if a person’s own risk of dying from the novel coronavirus is relatively low, getting infected means you could spread it to those at much higher risk.
It’s important for all of us to call out faulty interpretations and wrongheaded conclusions based on reported numbers. I’d love to see readers point out erroneous uses of COVID-19 data in the media or by public figures. The more we educate ourselves and help others understand the relative risks of different behaviors and activities, the better off we’ll all be.
I look forward to your insights on these questions.
Editor’s note: The reader who submits the most interesting, creative or insightful solution (as judged by the columnist) in the comments section will receive a Quanta Magazine T-shirt or one of the two Quanta books, Alice and Bob Meet the Wall of Fire or The Prime Number Conspiracy (winner’s choice). And if you’d like to suggest a favorite puzzle for a future Insights column, submit it as a comment below, clearly marked “NEW PUZZLE SUGGESTION.” (It will not appear online, so solutions to the puzzle above should be submitted separately.) Update: The solution has been published here.
Note that we may hold comments for the first day or two to allow for independent contributions by readers.