March 15, 2020

12% UPDATE: The Rule of 70 and Why Your Hospitals are Bracing for the COVID Tsunami.

Math helps us understand disease spread in populations. Confirmed cases of COVID19 as of 3/17/2020. 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. Actual cases in a population spreading COVID19 may be 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 )
3/30/2020 UPDATE: Based on the last 24 hours the fatality increase from COVID19 was 12%, which was what I used here on 3/15/2020 for this article's original post for estimating how fast ICU beds can fill up in any hospital. Math, and knowledge is power to prepare. "Fear is a reaction, courage is a decision." Winston Churchill

The Rule of 70? Maybe you are not a science person. Maybe more business, finance, and accounting, or more in the arts and theatre. 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 ICU patients in the space of just one or two weeks. Not just all the hospital's ICU beds, but all of its beds. Why social distancing and isolation is essential now, without cheating and going to clubs, concerts, restaurants or large gatherings. 
The rule of 70 is simple. 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 many world populations so far indicates a doubling time of 5 to 7 days, so let us use 6 days as the average. 70 /  12% growth per day gives us 6 days. 

"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 very large hospital with very large number of 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. 


How the doubling time of 6 days takes a hospital from 15 ICU cases to 450 in only four weeks. Even with 100 ICU beds, the system is now 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 non-ICU beds. There are not enough ventilators to help prevent many patients from dying. Also, typical car accident patients, heart attack victims, other seriously ill patients go to Emergency Rooms which are already mostly filled with COVID19 patients and there are no more ICU beds, and even no regular beds available. Health care staff are also getting ill and soon doctors, nurses, and their assistants are become exhausted too. The result is that the death rate from the illness increases because patients cannot get the ideal medical attention and resources they would have when the ICU is not overwhelmed. 

The result is what is being experienced now in Italy, 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 has been happening at his hospital. 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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