November 11, 2020

November 2020: The Rule of 70 and Why Your Hospitals are Feeling the COVID Tsunami Second Wave

Math helps us understand disease spread in populations. A historical view of the rise in cases of COVID19 as the first wave hit in March 2020. The apparent and surprising rise in cases after a long period of just a few cases is typical of the exponential nature of pandemic disease spread in populations. US data seems to have an instant-looking start because there was no significant amount of patient testing, then testing is being increased. Back in March, the actual cases in a population spreading COVID19 were increasing at 12% a day, which the Rule of 70 tells us is a doubling every 6 days. (Graph by KPMitton from CSSEGIS COVID19 data )

1/11/2020 UPDATE: 

This is an update of a posting I wrote back in March 2020 in the first wave of COVID19 just rising mostly in states where COVID19 first arrived. We are in danger again of having local hot spot states now like North Dakota, South Dakota, Texas, where the percent daily increases in cases exceed 5% per day. Early in 2020, we were up to a national average of 12% per day in the first wave. Rates one month ago had dropped well below 1% but now the average US daily increase in cases over last week had risen to 1.5 % per day, but that is the average of all 50 states. In hot states now we are having community locations with over 5% daily increases, and the experience in March will now happen again in November and December 2020. When you have a constant percent daily increase in case number, this percentage factor leads to an acceleration in numbers that can easily and suddenly fill a hospital. Here is the reason, the simple math behind it all. The Rule of 70. 

Maybe you are not a science person. Maybe more business, finance, and accounting. Maybe you are in the trades or other technologies or the culinary arts. Maybe you are familiar with getting a mortgage, or the stock market, bonds, and compound interest? Well, then you may already be familiar with the Rule of 70, which can show how the United States and many other countries can find themselves overwhelmed by intensive care unit (ICU) patients in the space of just one or two weeks. Not just all your local hospital's ICU beds, but ALL of its beds. This is why social distancing, quarantine, mask-wearing is essential now, without cheating and going to clubs, concerts, restaurants, or large gatherings of people. 

Here is how you use the Rule of 70. If you know the percentage growth rate of anything, like population, or patients infected by a pandemic disease, then 70 divided by the percentage growth rate will give you the doubling time. In the case of COVID19, the spread of infection in U.S. and world hot spots indicates that a doubling time of 5 to 7 days can occur. The Rule of 70 lets us calculate the doubling time. If we have a 12% growth rate per day, then 70 / 12% growth per day gives us 6 days. Some hot spots in the United States will be experiencing 5-12% case number increase per day.

"Twelve percent," you say, "Is that bad?" Yes, because once you see just a few COVID19 patients admitted to a hospital's intensive care unit (ICU), the 12% per day growth rate works like compound interest. The result is that a large hospital with many ICU beds, even 100, will be overloaded in just a few weeks. Doubling in growth is essentially an exponential process. A gentle sloping increase in numbers can go on for many weeks, and then quickly in the space of two weeks, such a hospital may have all its ICU full of critical patients. Then all the other beds in the hospital too. We do not have a ventilator available for every bed in a hospital, and yet most admitted patients may need a ventilator to have a chance to recover. This is in fact what has happened in Northern Italy, Spain and any country not taking preparation seriously. 

Example of how a doubling time of 6 days takes a hospital from 15 ICU cases to 450 in only four weeks. Even with 100 ICU beds, this model system is overloaded by 4-times its capacity. Most critical care patients will not have a required ventilator system and death rates become much higher than if the ICU capacity is never reached. The flattening of that curve, lower amounts over longer times, is only achieved by the population actively participating in social distancing. 

The above graph is from a spreadsheet I prepared for use by teachers or anyone. (See links at the end of this article). As you can see in this graph, the hospital's ICU has 15 COVID patients on day 1. Even one week later, this very large hospital has less than 50 critical patients and less than 100 after two weeks. Then they are suddenly overwhelmed over capacity by about 50 patients in week-3 and in week-4 there are more ICU patients than there are hospital beds. There are not enough ventilators to help prevent many patients from dying. 

This kind of situation also causes more deaths from all the other illnesses and accidents that occur in our communities normally. Car accident patients, heart attack victims, and other seriously ill patients go to Emergency Rooms which are mostly filled with COVID19 patients possibly with no more ICU beds, and maybe even no regular beds available. Front-line health care staff get ill and soon our doctors, nurses, and their assistants are becoming exhausted too. The result is that the death rate from non-Covid19 illness increases because patients cannot get the optimal medical attention and resources they would have when the hospital is not overburdened. 

The result is what was experienced in Italy early in 2020, a very modern country with a very modern and well-equipped health care system on par with the United States. Italy, in retrospect, did not enforce social distancing, they left it to be voluntary and many people traveled, went on vacations, went to clubs and restaurants, and spread COVID19 even faster. If you feel quite fine now while you are reading this, you may still have COVID19 but be asymptomatic for up to two weeks. At this time you and I could be potentially spreading it to others at home and at work. The "bomb" of patients will be seeded and then suddenly and exponentially explode in our hospitals in a few weeks. 

I recommend reading the following article that contains an English translation of an Italian MD's Facebook posting about what happening at his hospital earlier in the year. If you have friends or family who are skeptical about our need to prevent the spread of this disease, please share this information with them. By doing so, you will be contributing to saving someone's grandparent, parent, sibling, or child. Maybe even your own. Be a part of breaking the chain. We can do that, together. 

Italian Doctor's Coronavirus Experience - by Annie Reneau

Rule of 70 Lesson Sheet - Model of Communicable Disease Population Increase, CLICK HERE to get the google sheet or here to download the Excel version

Ken Mitton
Professor of Biomedical Sciences

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