Maths Helps to Explain Covid- 19 – maths is everywhere in our everyday life

Mathematics modelling can help us understand how the pandemic Covid-19 spreads out.

This infectious disease spreads from person to person. If, on average, every person who gets it goes on to infect two other people, then you have an epidemic. Two becomes four, four becomes eight, which becomes 16, which becomes 32……etc.

This is exponential growth and it is exactly what we are seeing in places like the United States and some countries in Europe. In these countries, every person who gets Covid-19 is going on to infect two-and-a-half other people on average. The result is that the number of infected people in these countries is doubling every few days.

This is the first time that humans have encountered the virus that causes Covid-19. As far as we know none of us have acquired immunity to it yet, which means the virus can infect all of us. With no immunity, the exponential growth of infections could go on for months.

In mathematics, exponential growth means a quantity that increases with a rate proportional to its current size. As the quantity increases so does that rate at which it grows. The more infected people we have in the early stages of a disease outbreak, the more people they will infect and the more the cases will rise.

Take a look at the diagrams of exponential growth at the rate of doubling up every day, and the diagram shows the U.S. Covid-19 growing rate within two and half months.  We can see exponential growth starts slowly and steadily, once it reaches a turning point, the growth would increase sharply, and within a short time it could reach a very large quantity.  

The following table shows an exponential growth within 30 days if the quantities doubles up everyday.  After 30 days, the total amount reaches 1,073,741,824, and the 31st day would be over two billions.  Of course this is the theory, presume the growth is not interfered by any forces.

In reality, with actions such as social distancing, wash hands and border control, the speed of exponential growth of the disease spreading can be slowed down and the damage can be reduced.  Australia is doing a good job in “flattening the curve”.