Corona 19 epidemic solved mathematically

Corona 19 is spreading out of China since the end of January. The YouTube Math Commentary Channel (3Blue1Brown) released a graph that summarizes the number of infected people in the region excluding China, explaining that it is increasing exponentially in a month and a half.

If you look at the trend of the total number of infected people excluding mainland China from January 22 to March 6 in the video, it is pointed out that the number of infected people per day has increased from 1.15 to 1.25 times from the previous day, increasing exponentially. N is the number of infected people per day, E is the average number of people who are in contact with each day, and P is the probability of getting infected by contact with the infected person. have. d is a variable representing the date.

If this equation is expressed as Nd+1=Nd+E·p·Nd, Nd+1=(1+E·p)Nd, Nd is the number of infected one day, and Nd+1 is the number of infected after 1 day. 1+E·p can be expressed as an increase in the number of infected people. N is, the more infected people per day, the faster the infection can spread.

How fast the number of infected people is increasing is that the number of infected people increases from 100 to 1,000 in 20 days, and the number of infected people increases from 1,000 to 10,000 in 13 days. Looking at the slope of the graph, it is predicted that the number of infected people will increase 10 times every 16 days on average. If the number of infected people continues to multiply 10 times every 16 days, after the 30th, that is, 1 million people around April 5, 2020, 10 million people 47 days later, April 22, and 100 million people on May 9 after 64 days, On May 26, after the 81st, it will reach 1 billion.

Of course, this does not mean that this increase will continue. The number of people infected with Severe Acute Respiratory Syndrome SARS converged at 8,000, and the Spanish flu spread to 500 million people, 27% of the world’s population at the time. The infection from Corona 19 is also likely to converge somewhere, and the question is when will that be? Also, the number of infected people does not necessarily exceed the global population. Starting from the inflection point, the rate of increase begins to decrease.

While the number of infected people is increasing, the number of infected one day exceeds growth factor 1 divided by the number of infected the previous day.So, for example, the growth factor on March 4 is the value obtained by dividing 2,964 people infected on March 4 by 2,159 infected people on March 3. It is 1.37. When the growth factor exceeds 1, the logistic curve increases exponentially, and when it is less than 1, it turns toward convergence. For example, if the number of infected people is currently 21,000, and the growth factor is maintained at 1.15, the number of infected people after 61 days could exceed 100 million. Even if the growth factor drops to 1.05, the number of infected people after 61 days is 400,000.

In the end, you have to think about what to do to lower the growth factor. Individuals should avoid going out such as traveling, go to places where people gather, and wash their hands frequently.