[SIR model analysis] Determination of γ * (R-1) and peak out of infection number ♬ World edition

Japan has finally issued a state of emergency. On the other hand, recently, we have heard news that the number of infections is peaking out one after another in South Korea, Italy, Spain, etc., following China. Again, based on the following SIR model, we analyzed the number of infections, cures, and deaths worldwide.

{\begin{align}
\frac{dS}{dt} &= -\gamma R I \\
\frac{dI}{dt} &=  \gamma (R - 1) I \\
\frac{dr}{dt} &=  \gamma I \\
\end{align} 
}

So, today I decided to apply Model analysis of the other day to the total value in the world. For the theory, see the previous article. The results are as follows. First of all, this figure is a figure in which the number of infections is likely to reach 10 million in about January if it continues to grow. However, if you look closely, you can see that it has the following characteristics. What you can see from this graph (1) Looking at the graph of the number of red infections in the above figure, the first peak is the peak in China, and this time it is about to become the second peak in the world. However, it is still increasing. (2) Looking at the healing curve, this also once crossed the red line with the end of China, but the red line increased sharply again, and healing began to slowly follow after that. ③ The curve of I / (R + I) once fell below 1, but now it is horizontal around 3. However, it seems that he came here and had a slight negative inclination. In other words, it seems to indicate that it has begun to end. (4) It can be seen that the graph below shows a gradual change between the effective reproduction number R = 1.5-10. However, recently it is a large value of about 8, and it can be said that it is still strongly infected. ⑤ γ has recently decreased to around 0.015 for the second time, which is similar to the behavior in China and seems to be the behavior per the peak number of infections.

Finally, the value of γ (R-1) can be understood to some extent on a logarithmic scale, but what I want to know is when it passes 0, so I drew it on a linear scale. The results are as follows. In other words, it is decreasing linearly, and the number of infections in the world will peak out in about 10 days. The peak out is not the end.

Moreover, the number of new patients in Japan today has reached 500. I will continue to tighten my mind ・ Do not go out ・ Do not gather ·mask ・ Hand wash I hope that the world will be released from COVID-19 as soon as possible.