Urology Pearls: COVID-19 goes exponential

Shahar Madjar, MD

For a moment I thought that we, the people of the Upper Peninsula of Michigan, have escaped the wrath of Covid-19. It was an overly optimistic belief based on unfounded hope and misconception.

I relied on geography. I drew a map of the UP in my mind-a long and narrow strip of land separating Lake Superior from Lake Michigan with a short border at its western end; and on the east, a tip pointing to infinity, and a single bridge. Surrounded by water from all sides but one, I believed the UP to be remote enough and isolated-an ideal place to hide from an impending disaster.

I relied on demographics. A population of only 300,000. Thinly, sparsely spread. I found consolation in thinking like a virus: why, for God’s sake, would I choose the UP, of all places, where the people are few and far apart.

And last, I relied on Dawn, my office manager, who had married a man of Finnish descent. He had told her that if everyone were to behave like Finns, the virus wouldn’t stand a chance. Finns, she said, unlike the French, Italians, and the Russians, keep a safe distance from others. I thought to myself, the UP is half-an-island, each of us is an island, so Covid-19 is doomed!

Then I remembered that when dealing with a virus, math must also play a role. Its role is exponential and therefore counter-intuitive. Let me explain: most people are familiar with the concept of linear growth. We grow old in a linear fashion-each birthday marks the addition of a calendar year. We typically make friends and fall in love in a linear fashion-one person at a time. Every life journey starts with a first step, but the road is taken one stride after another. We are experiencing life along relatively straight lines. Linear growth feels normal, it is natural. It is easily understood because it is familiar.

But not everything grows in a linear fashion. The spread of Covid-19, for example, doesn’t follow a linear growth pattern. It grows exponentially! What does it mean? Here is an example: Suppose you deposit $100 in a bank account for ten years. The bank gives you two options. The first: you will be given 10% of your original deposit each year ($10 a year). Your money will grow steadily, in a linear fashion, and at the end of the ten year period, you will double your money (to $200).

The second option is that you will accrue compound interest of 10% a year. After one year you will have $110, which will serve as the basis for the interest earned for the second year (110% of $110, or $121 rather than merely $120), and so on. Your money will grow exponentially, until the end of the ten year period, you will have a whopping $259. It is no wonder that Albert Einstein considered compound interest the most powerful force in the universe!

The rate of transmission of Covid 19 is expressed by the R number, or Reproduction number. It measures the spread of an infection in a population. If R is two, for example, two infected people will infect four other people who will infect eight others, and so on. The numbers will grow exponentially. If R is greater than 1, Covid-19 will spread quickly; if it is lower than 1, infections will slow. In Michigan, the R number right now is 1.23, which means that the number of tests positive for Covid-19 has shot up dramatically. The number of positive tests is a leading indicator. The number of hospitalizations, and deaths are soon to follow.

For a moment I thought that the UP had escaped the frightening fate of Covid-19. But a few cases have snuck into the UP, and that was enough. The number of cases has spiked and continues to rise. This growth is exponential and therefore hard to grasp, but the numbers speak for themselves and there is no place for denial.

However, there is good news too. Initial results from the manufacturers of vaccines are promising. Until these vaccines are widely available, though, I urge you to follow these basic guidelines: wear masks, wash hands, avoid crowds, and stay apart. We aren’t immune to the pandemic. Be a good neighbor. Be a little island.


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