I recently posted a link to a more easily understandable display of Covid-19 infections and deaths for every country. (Incidentally its creator, a high school student, had a brief profile written about him in the latest issue of The New Yorker.) But one thing it lacked was the ability to visualize the differential rates of growth in each country over time to better enable us to understand how the disease is spreading and what is meant when people say that one region lags behind another by so many days, and how to know if containment methods are successful.
Part of the problem is that exponential growth is not intuitive to understand even though we have some everyday examples of it. The most common one is compound interest in a savings account. If you leave the principal untouched, it will grow slowly at first and then increasingly rapidly so that over a long time one can accumulate quite a lot. But despite that, when it comes to change, we tend to think in linear terms because many things change in close to linear fashion and it is very simple to understand and the human mind tends to grab on to simple ideas and explanations and try and force everything into that mode. But there are times, and this coronavirus pandemic is one, when the amount of change in some thing in a given period is proportional to how much of that thing exists at that moment (which is how compound interest works), and then you have exponential growth.
To better understand exponential growth and its application to the pandemic statistics and how to tell when the data shows that a country has managed to brings things under control, this video is helpful because it illustrates when the inflection point (i.e., when the rate of growth of cases starts to decrease) is reached.
The excellent time-lapse growth chart shown in the above video can be seen here and is being constantly updated. It enables us to see at once that China and South Korea seem to have been successful in curbing the pandemic’s growth. Japan and Iran seemed to show some success at one time but it looks like they have lost some ground.
The explosive nature of exponential growth is hard to fully comprehend, as can be seen in the answers given to a problem like this.
A lake has algae growing on its surface. The amount of new algae that appears in a 24 hour period is equal to the amount that existed at the beginning of that period. i.e., the amount doubles every day. If the lake starts with almost no algae but is fully covered by day 30, when was it only covering a quarter of the surface?
The answer is day 28. But some people, unless they pause and think things through, would tend to give an answer that is close to about 8 days because they are thinking linearly.