It’s easier to deal with a situation if you have a realistic understanding of what you are up against. I have spent my professional life introducing teenagers to challenging technical subjects and, with this opinion piece, I’m taking a crack at discussing the spread of infectious diseases, such as COVID-19, with the wider audience. I hope you will be patient with me if I retread ground that is already familiar to you.

The human mind typically thinks in terms of what mathematicians call a “linear” process. In linear growth a fixed increment of change is added to the total output for each unit of time that passes. To illustrate, let’s play like a virus spreads according to a linear growth pattern with one new case added to the total for each day that passes. If we start with one case of the disease on day one there will be two cases by day 2, three cases by day 3, and so forth up to say 16 cases by day 16. The human mind easily copes with this type of model and attempts to apply it to any kind of growth process. However, diseases don’t spread through a population in a linear fashion — they spread exponentially.

Instead of additive increments, exponential growth is characterized by “doubling times,” and the output doubles with the passage of each doubling time. Returning to our hypothetical example from above, let’s once again start with one case on day 1 and assume a doubling time of 1 day. There would again be two cases on day 2, but four on day 3, eight on day 4, 16 on day 5, on up to 32,768 cases on day 16 (that is somewhat less than the estimated population of Cowley County). On day 17, there would be 65,536 cases. The spread of the disease starts slow, lulling us into a false sense of security, but soon accelerates to a terrifying level. Understanding exponential growth does not come naturally to the human mind, but treating exponential processes as though they were linear can lead to devastating errors of judgment. As an aside, compound interest follows this same basic law, which is probably why so few of us truly understand how our mortgages, vehicle loans, and IRA’s work. It is also the reason people erroneously assume that there is no immediate call for alarm in the early stages of an infectious disease outbreak when the case count is still small.

We can use the above example to illustrate the critical importance of slowing the transmission rate of a disease and, thus, increasing the doubling time for its spread as much as possible. For instance, if the doubling time in the above example were 2 days, instead of 1, the number of cases on day 16 would be only 181 and we wouldn’t reach 32,768 cases until day 31. That would help smooth out the demand on medical resources and buy more time to develop new therapies and, eventually, a vaccine.

Finally, for COVID-19 it is rather easy to dramatically lower the rate of transmission and increase the doubling time, but we all must do 4 simple things: wear a mask or other face covering in public, maintain a social distance of 6 feet whenever possible, wash our hands frequently, and avoid touching our faces as much as possible. Each of these measures may be a bit annoying at first, but they quickly become habitual and our accumulated experience with the disease has indicated that they are very effective in slowing the spread of the virus. Once again, however, for them to work their magic we all must participate. Given the current situation (3,290,000 cases in the U.S., with 137,000 deaths recorded at this writing), is it asking too much that we all do these things both for ourselves and each other?

I will close by commending the Winfield City Commission for having the courage to pass a mask ordinance last week and I urge the other units of local government in Cowley County to do the same.

 

David R. Stinemetze

Arkansas City

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