Even a fatality rate of 1% would leave everyone touched with tragedy, mathematics professor says
I was not worried about the previous outbreaks such as SARS or H1N1. However, I’ve watched with interest and horror since COVID-19 started spreading in the Wuhan province of China a few months ago. What grabbed my attention is its ability to spread via people not showing symptoms and its long incubation period, enabling it to hide and spread throughout a community without being detected until it’s too late. Still, I assumed that by the time it reached the U.S., that we would be fully prepared with personal protective equipment such as masks, as well as testing equipment, to prevent COVID-19 from hiding and spreading “in the shadows.” Unfortunately, for whatever reason, those assumptions were not correct.
We will now do the best we can, given our current situation. It will take a lot of effort from many people, and a big part of doing our best is to know what we are up against. The lag time between getting the virus and showing symptoms is a crucial element that cannot be overlooked, as we plan what we must collectively do in the next several months. Human nature suggests that we will more willingly comply with the sacrifices we should make, if we have a better understanding of what’s really happening.
The first mathematical principle to understand better is exponential growth — growth at a rate proportional to how much is already there.
I am a professional mathematician, but not a professional mathematical modeler of infectious diseases. This post consists of a couple of observations from being generally aware of mathematical principles. With regard to specifics, I defer completely to the trained specialized experts, and I hope we all defer to these experts.
Everything I’ve read suggests that without strong intervention, the number of cases will roughly follow an exponential growth model, at least at the beginning. Therefore, the first mathematical principle to understand better is exponential growth. It is often confused with extremely large or fast growth. In fact, it does not necessarily mean that at all. Rather, it means growth at a rate proportional to how much is already there. So, if hardly anyone has COVID-19, then the growth rate of the infected population is extremely small, and that’s the problem — exponential growth is sneaky in a way that adds to the other inherent invisibility of the danger of this virus. A small number of cases means that we may not notice it. As soon as we do notice it, the (proportional) growth rate is also noticeable, i.e., not small. Now we are at the mercy of accepting all the spread throughout the population that the virus has achieved during its undetected lag time of several days.
So, one of the keys is, how much growth happens during this lag time? Suppose a hospital is at one-eighth of its capacity, but the number of cases doubles every three days. Since treatment for COVID-19 can require weeks of hospitalization (A New England Journal of Medicine article from March 30 showed that the median length of hospital stay for COVID-19 survivors in Seattle was 17 days) the same hospital could be at capacity just nine days later, and overwhelmed in 12 days. If social distancing increases the number of days required to double the number of cases from three to five, then some of the original patients will have recovered and left so that the hospital can save more lives. If social distancing is well-coordinated, the number of cases might cease to approximately follow an exponential growth model at all.
My point here is that a hospital that appears to be empty, may be on the verge of being overwhelmed, leading to an increased fatality rate. Having a mathematical awareness of exponential growth generally helps one to take this very seriously. “Flattening the curve” is about increasing the number of people that medical professionals can treat and therefore save. It’s also about delaying infection, in case we find treatments or vaccines during this delay.
The 1% fallacy
There is one other feature of the greater discussion that has left me needing to say something as a mathematics educator. A fatality rate of 1% is not small — it’s huge! I’ve seen people struggle with this, so I’d like to cast it as simply and concretely as possible. If you make a list of the people who are directly important in your life in a typical month — family, classmates, co-workers, teammates, club members and friends — this list may have 150 people on it. So, we have a good sense of numbers less than 200.
If half of the U.S. gets COVID-19 and there is a 1% fatality rate, then that’s 1 out of 200 people in the next 12 months, which is enough to affect every one of us deeply and personally! I should not need to know the number of fatalities to know that this is totally unacceptable. The benefit of using a percentage is that it puts everything nicely in context for those of us with 100 to 200 people in our orbit. These projected COVID-19 deaths are all in the next year and the anticipated strain on health services may increase fatality rates for many other ailments as well.
Since all of us can contribute to a healthier society, and none of can clearly see the future, I ask that we realize this will be over soon enough, probably within a year. Please don’t get frustrated if we are asked to go through social distancing more than one time. It will be worth it!
Finally, as a mathematics advocate and educator, I point out that having an awareness of mathematics clarifies what is happening in an approximate way, on an intuitive, human level. It would be helpful if we all had more of this awareness! Best wishes and keep healthy.
Dr. Dan McQuillan is a Charles A. Dana professor of mathematics at Norwich University.
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