Coronavirus: Flatten the Curve, Delay the Onset

Coronavirus:

Spread Out the Cases to Flatten the Curve

and

Delay the Onset

Some disclaimers and miscellaneous comments:

I AM NOT A MEDICAL DOCTOR. None of the following should be construed as medical advice, or actual pandemic data, or risk assessment for any person or group of people. I suppose I could have used the acronym IANAMD but I don’t find that nearly as entertaining as the acronym for I Am Not A Lawyer. However, IANAD (I am not a diplomat). You may not enjoy my attempts at humor, but IMHO, even serious topics sometimes need comic relief.

First, what does it mean to spread out the cases and flatten the curve? This discussion is for those folks that think “If you’re gonna get it, you’re gonna get it. Might as well get it over with.” Fatalism: No matter what we do, if some percentage, say 70%, will become infected eventually, then why should we do anything? 

            It’s not that simple. The news provides us with a perfect case study. Then comes the hospital analogy. The numbers shown were selected for ease of computation. The conceit is scalable.

Consider the Case of the Cases of Toilet Paper at Your Local Costco: Suppose during March each year that your local Costco sells (on average) 930 cases of toilet paper. If demand is relatively stable, then the store may not keep more than 120 cases in stock and on display, after all, display space is storage space in a warehouse, and that space is very valuable. Now, if on average, the store sells 30 cases per day, delivery trucks arriving every 4 days can easily keep the local Costco supplied with cases of toilet paper to buy. At 30 per day, limited one to a customer, the store easily manages the sale of 930 cases for March. Both Costco and 930 customers are happy. Next consider what happens when Faux News sensationalizes a shortage story, and all 930 customers, and perhaps a lot more who were not going to buy toilet paper until April, show up on the day of the most recent delivery and want to buy not their usual 1 case but 2 or 3 cases. With only 120 cases is stock, at least 810 or more customers will be disappointed. Perhaps so disappointed that they will then converge on the Costco across town. When the purchases were spread out, the supply line kept the stocks shelved. So long as the demand averaged less than 30 cases per day, the supplies were more than adequate. When people panicked and overloaded the sales facilities, shortages occurred and more panic ensued. Spread out buying for 930 people worked well.  Having all 930 people show up at once broke the system.

If Costco has known three weeks in advance that 930 people planned to show up a given Tuesday, they probably could have arranged to stock extra cases in the parking lot. The ability to plan in advance of heavy demand helps, but it has limits farther up the line.

Consider the Case of the Coronavirus Pandemic at Your Local Hospital: Imagine that a hospital in your town (perhaps the only hospital nearby) has a bed capacity of 93. However, only 30 of those offer any hope of isolating patients with a contagious infection. Of those 30, only 10 are also intensive care. Suppose over the next 50 weeks that 600 infected patients require hospitalization and that of them 100 require intensive care. Also imagine that staffing and supplies are adequate for this many beds. So long as each infected patient’s stay averages no more than two weeks, and the occupancy rate is spread out, never exceeding 30 for infected including 10 for intensive case, the hospital should be able to handle the patient load. But what happens if all 600 of these patients get sick within a week of each other and show up in March? Not only is there no room for all of them in isolation, the entire hospital has only 93 rooms. Life snd Death Panic ensues, and there is no hope in waiting for the next shipment of rooms to come in.

If the hospital had known six months in advance that 600 patients were going to show up almost all at once in March, their best bet would be to rent an unused cruise ship and fix up the suites to serve as isolation rooms. However, they would have a hard time hauling in extra staff to cover the floors. Probably someone would remark that only 50 or 60 of the 600 would likely die, so it was just not worth the expense.

Pandemics don’t usually give you six months notices anyway.

What if the hospital had known 10 years in advance that pandemic would eventually arrive? As a society, we’ve known at least a hundred years in advance, since the Spanish Flu of 1918 where 50 million died, that there would be another deadly pandemic. It is here.

Perhaps we would be lucky enough to have experts planning strategies for such events. Yes, we did, but no, we wouldn’t listen. In fact, some of these experts were recently downsized. Besides we don’t like experts. After all, we’ve had years of expert warnings about climate change, and have attempted almost no remediation. In fact, we reversed our few attempts because we also don’t like regulations. So forget this paragraph. Pandemics and climate disasters don’t yield to a business-like approach because “It costs too much”, “Where’s my profit”, and “Who knew it was so complicated?”

However, there are good reasons for working for a time-shift and delay approach to pandemics. You’ve probably seen side-by-side bell curves demonstrating the advantages of spreading out the total demand over time compared to having the demand peak in a short period of time.  What may be overlooked in those bell curves comparisons of peak demand, is that the spread-out curve is also shifted right. In other words, the increase in infection numbers is delayed for as long as possible. This gives time to plan, for which we might spend money once panic is tangible. And it gives times to develop vaccines or cures for the future. With enough delay, it might even allow enough time for medical advances to reduce the fatalities for the current pandemic.

How do you delay the inevitable infection and spread out the curve. Do the usual stuff you see from medical advisers when you Google Coronavirus, including wash your hands, don’t touch your face, stay away from crowds (social distancing), self-quarantine or wear a mask in public if infected, don’t bother wearing a mask if you are not infected unless  you wear goggles too to stop the droplets, etc.

Moreover, don’t expect God to save you or your loved ones from your own stupidity. Miracles like that occur no more often than random events.

The chance that a pandemic will not affect your life at all is small. You might not die yourself, but…. Now follows a few mathematical examples for those self-centered fatalists who have decided that the risk of death from the Coronavirus to their own life is so small, that they will ride a bus into town, spend the evening screaming in a crowded auditorium, drink wine from the shared communion cup at church the next morning, and then visit their aging grandparents. Others, who might also benefit from a little math homework are  those who get medical advice from Faux News.

And now a quick and dirty probability primer for our times. 

I worked on this longer then I intended, so you might want to check my arithmetic:

Some of the Coronavirus death rates in the following examples are my crude adaptation of values I’ve read in the news. Don’t bother to dispute them. I don’t expect them to be correct. However, different rates will not alter the way the probabilities are calculated, only the results. The Coronavirus infection rate of 70% was a convenient arbitrary number I selected for these examples. Actual infection rates are influenced by too many factors for me to do more than just guess. If there is a consensus for the infection rate, I am unaware of it. Besides I expect it to shift around before it is estimated after the main pandemic is over, so please don’t bother to offer another value.

Most gamblers know the following simple rules of probability which assume that A and B are independent events, each with a “known” probability:

Probability Rule 1: If the probability of an event A is X%, then the probability of A NOT happening is 100% - X%.

Example 1-1: If the probability of Dick getting infected by the Coronavirus is 70%, then the probability of Ted NOT getting infected is 100% - 70% = 30%. (Or 1.0-0.7=0.3)

I won’t attempt to calculate the probability of Dick’s wife, Jane, getting the virus given that Dick has already caught the virus. That is far too complicated. Let’s just assume it is very high, and that Dick is in deep shit.

Example 1-2: Suppose that the probability, the chance, of someone dying from a Coronavirus infection is 1%. Then the probability of them NOT dying is 100% - 1% = 99%

Suppose that the probability of someone dying from a Coronavirus infection is 2%. Then the probability of them NOT dying is 100% - 2% = 98%

Suppose that the probability of someone with underlying conditions dying is 10%. Then the probability of them not dying is 90%. Similarly, a 15% chance of dying goes with an 85% chance of not dying.

Where did I get these probabilities of dying? Usually they come from observation of what happens in earlier infections. If someone observes that of 1000 folks infected, 10 die, then the observed death rate is 10/1000 = 0.01 = 1%, and 1% then looks like a good estimate of the probability of dying. If out of 100 high risk patients observed who have the virus, 10 die then 10/100 = 10% seems like a good estimate for the probability of a high risk patient dying. But I didn’t do the observations or calculate the rates myself. I read something similar in the news.

Simple Probability Rule 2 (Also known as the multiplication property, often associated with the word AND): The Probability that A AND B both happen is the probability of A multiplied times the probability of B.

Example 2-1: Suppose Jack is at high risk for dying from the Coronavirus infection (probability of 10% dying, 90% living) but Jill is regular risk (probability of 1% dying and 99% living).  Then if both of them are infected, the probability that they both live is the product of the probability of each living individually. In other words, the probability that Jack AND Jill both live is 0.90 times 0.99  = 0.891or about 89% for the probability that Jack lives AND Jill lives.

What does “NOT both live” mean? The usually interpretation is that at least one (maybe both) die. This makes the probability that at least one of them dies to be about 100%-89% =11%. This does not mean that 11% of two people (Jack and Jill die). 11% of 2 people is 0.22 person. Not a reasonable outcome.

First of all notice that the 10% and 1% death rates are based on limited observations and are certainly subject to change as more observations become available.  Nonetheless, the usual interpretation of predicting what will happen with a calculated probability like 11% is to express that predictor over a large number of similar cases. So if I observe 100 infected couples LIKE Jack and Jill, then I EXPECT ON AVERAGE that 11% of those 100 couples, which is 11 couples, will have at least one member of that couple to die. Will that actually happen for a particular group of 100 couples? Will exactly 11 coupes experience tragedy? I don’t know. Statistics don’t apply well to a specific individual case. Even with 100 couples observed, expect the prediction of 11% to be close but not perfect. Rather apply the prediction as an average over the long run. If I observe 1000 such infected couples, I expect the 11% estimate to improve at observing1000 couples rather than 100 by the Law of Large Numbers.

Example 2-2. Consider a family of five: a Mom, a Dad, a Son, a Daughter, and a Grandma. The Coronavirus comes to the house and infects everyone except Mom (she washes her hands a lot) whom is thus not included in the calculations: If you do not contract the virus, the probability of dying from the virus is 0%. Dad is in a regular risk group with a probability that 1% will die (99% live). The kids are very low risk with a probability of 0.1% dying (99.9% live). Grandma is in an extremely high risk group with a probability that 15% die (85% live). Then the probability that all four of the infected live (Dad AND Son AND Daughter AND Grandma live) is 99% times 99.9% times 99.9% times 85% = (0.99)(0.999)(0.999)(0.85) =0.79 = 79%. The probability is 79% that all four infected live. In other words, the probability that at least one family member dies of Coronavirus is 21%. Grandma seems to be the most likely candidate, but we're not guaranteed that. It is even possible, but extremely unlikely, that all four of the infected members die.

Example 2-3: The usual probability assigned to getting a head on a single coin flip is 50%. Similarly, not getting a head is 100%-50% = 50%. I ignore such highly unlikely distractions as landing on edge and losing the coin. What if I flip a coin four times? What is the probability that all four flips come up heads? Basically this is the probability of getting a head AND head AND head AND head. Hence, I multiply the probabilities for each individual flip: The probability of four heads in a row is 50% times 50% times 50% times 50% = (0.5)(0.5)(0.5)(0.5) = (0.5)^4 = 0.0625 = 6.25%. The probability of NOT getting four heads in a row is 100%-6.25% =93.75% which could also be interpreted as the probability of getting AT LEAST 1 OR MORE Tails in the four flips. (0.5)^4 is short hand for using 0.5 as a factor in a product 4 times. This is also known as exponent notation using 0.5 as the base (the factor) repeated 4 times as indicated by the exponent 4. I mention this because calculators usually have an exponent button to make the entry easier. Calculators are very useful for all but the simplest probability calculations. The probability of getting 10 heads in 10 flips (10 in a row) would be (by calculator) (0.5)^10 = 0.0009765625 or about 0.098%. Possible, but highly unlikely. Hence the probability of getting at least 1 tail in ten flips is 99.902%, almost a sure thing.

Example 2-4 Suppose that you have 13 low risk friends (Coronavirus 1% death rate, 99% live rate) whom you often hang with, and suppose that about 70% of the group (counting you make 14 total) catch Coronavirus. That’s 9.8 people in the group, let’s round that to10 (I deliberately avoid fractional people and hence fractional exponents). Then the probability that all 10 live (and hence no one in the group dies) is (0.99)^10=0.904382075 or about a 90% chance that all in the group will live. That leaves a 10% chance that at least one of you dies. If there are 2000 similar groups (20000 infected people total) in your area, then expect approximately 10% of the 2000 similar groups, 200 such groups, to suffer the tragedy of losing 1 or more members.

Recognize that any member of a group such as that described in this Example is likely the member of many other groups including those with members having a higher death rate risk from the Coronavirus. The more groups you belong to, the more likely you are to know at least one person who will die during the pandemic. The moral is that the Coronavirus is likely to affect your life, even if you do not get sick. If you don’t care about anyone else’s life, then at least consider how an economic recession as a result of the pandemic might affect you.  

Fifty million died of the Spanish flu pandemic in 1918. Even the then President, Woodrow Wilson, was stricken by the virus. Experts told us that other pandemics would come. They have,  but none since have been as deadly. Until now? Time will tell.

Coronavirus is here, an immediate threat to our society, to the lives and well-being of our people as well as to our economy. As individuals we can contribute to the fight against the pandemic, but only as a society acting together can we minimize the damage. This suggests a change from our usual mode of planning, funding, and providing healthcare. And among our considerations should be whether planned healthcare and responses for the entire society is ultimately cheaper than a piecemeal system with incompetent leadership. Perhaps this pandemic will teach us the answer, if we examine history and listen to real experts rather than TV pundits. I hope we do not avoid asking the needed questions because another pandemic is inevitable, and it might be worse than this one.