Sunday, March 22, 2020

Exponential Growth

                                                                                                written 15 March 2020
                                                                                            published 22 March 2020

            One of the standard discussions in financial planning is the "magic of compound interest".  If you put $1000 in a jar and add another $1000 every year, after a decade you will have $10,000.  But the same savings rate invested at 5%, compounded monthly, will produce $14,587 at the end of the decade, almost 50% increase.  That is an example of exponential growth.  
            There is an old story that the inventor of chess asked his king to reward him for his discovery with a quantity of rice.  A single rice grain was to be placed on the first square of the chessboard, two grains on the second square, four grains on the third, doubling on each square.  The reward could not be paid.  By the time you get to the 64th square, there are over 18 quintillion (million trillion) grains of rice on the board, weighing over 300 billion tons, 400 time the current annual planetary rice production.  This is an example of extreme exponential growth.
            Life produces exponential growth routinely.  A single apple seed grows to become a mature tree that can produce 500 apples a year for 20 years, an increase of ten thousand. A single grain of rice will produce as many as 100 new grains when it matures in as little as four months. Three crops a year would give an annual return of one million to one.  
            When we get down to the cellular level, things happen very rapidly.  Humans grow from a single cell to 37 trillion cells in 18 years, an amazing exponential growth rate.  Human cells take about 5 hours to divide, and our bodies produce about 10 billion cells every hour, for our entire life.  In a healthy body, this production balances out the number of cells that die, so our body size and weight remains relatively stable over time.
            Viruses, such as the flu, are one thousand times smaller than our cells.  An individual is called a viron, which is very simple in construction, consisting of a small quantity of nuclear material encased in a protein shell.  A single viron can infect a cell.  Once it penetrates the cell wall, it hijacks the cell systems to replicate the parts of itself.  This lysogenic cycle takes about 6 hours, then it moves into the lytic cycle, where the parts self-assemble into new virons, and burst out of the cell, generally killing the host cell.  Different viruses have different burst sizes.  Flu produces at least a thousand new virons in each infected cell, giving a possible growth rate of a trillion to one every day.  That is the challenge our immune system faces when we become infected.
            COVID-19 appears to be twice as infectious as normal flu, with estimates that an infected individual can infect 2-3 other people within two weeks.  Most infected people will have a mild case and may not even know they have the virus, but 15%-20% will have serious symptomatic responses, perhaps requiring hospital care.  Reported global case numbers are generally people diagnosed as a result of showing symptoms such as fever.  Of that group, almost 4% have died.  This means that the overall lethality rate may be 0.6% - 0.8%, which is 6 to 8 times greater than normal flu.  A precise lethality rate can't be determined at this time, since we have no idea how many people are actually infected, only how many show symptoms, and how many of those die.  Finally, estimates are that 40%-70% of the global population could be infected by the time this runs its' course.  The evidence so far is cause for concern and preparation, because exponential growth can rapidly change the magnitude of the problem, potentially overwhelming health care capacity.  
            The first case of US community transmission was reported on 27 February.  I am writing this on 15 March, 17 days later.  Today's reported US case total is 3,273, a 774 case increase from yesterday. Like the single grain of rice on the first square of the chess board, these first few days of reported cases seem modest, but exponential growth indicates an impending tsunami.  So far, our federal government's response has been to minimize the problem, because it reflects poorly on the president. Unfortunately, reality always prevails over self-serving denial.