[Introduction to infectious disease model] All parts of Japan are ending ... ♬

Today, the extension of the state of emergency is announced, but for the time being, I would like to suppress the situation nationwide as of today. Last time, we predicted the peak out of the number of infections based on the SIR model, but this time we would like to use the SIHR model to predict the termination. .. ** This article was also written by an amateur, so please handle the content at your own risk ** The SIHR model is an extension of the SIR model in order to reproduce the delay in the number of cures, and is as follows.

{\begin{align}
\frac{dS}{dt} &= -\beta \frac{SI}{N} \\
\frac{dI}{dt} &=  \beta \frac{SI}{N} -\gamma I \\
\frac{dH}{dt} &=  \gamma I-\delta I \\
\frac{dR}{dt} &=  \delta I \\
\end{align} 
}

In addition, most of the data is obtained from the following reference (1), and since the healing number data in Tokyo is an abnormal value, this is obtained from reference (2).

【reference】 ① Current status of new coronavirus infection (May 3, 2nd year of Reiwa) @ Ministry of Health, Labor and Welfare ② Status of domestic infection of new coronavirus @ Toyo Keizai Online And the data ③ and apps ④ and ⑤ used this time are placed below. ③ is composed of three files. In addition, ④ is an application that draws the general situation, and ⑤ is an application that fits this. ③COVID-19_Japan/data/ ④COVID-19_Japan/simple_draw_Japan.py ⑤COVID-19_Japan/fitting_SIHR_Japan.py

What i did

・ Situation in Japan ・ Situation in Tokyo ・ Situation in Osaka ・ Situation in Hokkaido ・ Situation in other areas

・ Situation in Japan

First, the general situation When drawn on a linear scale, as shown below, there is a large value at the left end of the bar graph of the number of new infections, but this is the total value of the data before March 25. So, this time I will analyze the second wave of infection that started on March 26th. Looking at the graph below, the number of infections (number of hospitalizations) is beginning to decrease just before 10,000 people. The following is a semi-logarithmic graph other than the bar graph. Solving this with the above differential equation gives the following. However, keep in mind that there are input parameter dependencies and the results you get will be different. Here, the number of new infections is displayed as an example. That is,

Basic reproduction number = 4.18\\
Effective reproduction number = 0.21\\
Infection rate\gamma (R-1)＝－3.49e^{-2}

Was obtained. Please note that this value depends on the parameters when fitting, so please handle it with care. In conclusion, the peak out of new infections has passed, and it seems that the number of new infections has just peaked and will continue to decline. Then, the number of infections and the number of cures cross each other in about 12 days, and it seems that about half of the number of infections (number of hospitalizations) will be reached in about 3 weeks. However, depending on the situation, the number of infections may not decrease and may change slowly, so it can be said that the extension of the national state of emergency is an unavoidable decision. It is difficult to know how to surely reach the end, but if we can fit in various ways and the number of infections and the number of cures can intersect as it is, it can be said that the situation will not return as the second wave, and I think that various things can be alleviated. However, I think that each region will have its own judgment, and it is necessary to continue the current lifestyle.

・ Situation in Tokyo

The general situation is as follows, and the 165 and 160 people on the right are really disappointed. For this reason, the whole thing seems to occur randomly. But, as it may be, ... Also, the number of cures has a step in the middle, and it seems that the data is not managed.

• The number of cures is one of the most important data directly linked to the collapse of medical care. However, the number of infections, cures, and deaths seems to be regular to some extent, so I will try fitting. The fitting results are as follows. The obtained quantities are as follows

Basic reproduction number = 3.82\\
Effective reproduction number = 0.32\\
Infection rate\gamma (R-1)＝－3.93e^{-2}

・ Situation in Osaka

In Osaka, you can see a step with a large number of Haruo. Apart from that, the number of new infections seems to have decreased. The results are as follows. The obtained quantities are as follows

Basic reproduction number = 4.18\\
Effective reproduction number = 0.59\\
Infection rate\gamma (R-1)＝－1.50e^{-2}

In Osaka as well, it is difficult to see if the number of cures will increase in the future until the end.

・ Situation in Hokkaido

Hokkaido was one of the cities where the spread of infection just started last time. Just by looking at the following overview, you can see that the situation is still severe. And the fitting result is as follows. By calculation, the number of new infections is near the peak, and the result seems to be saturated. The obtained quantities are as follows, and the effective reproduction number is slightly larger. And the peak number of infections is yet to come, and the number of cures is small, so the situation is unpredictable.

Basic reproduction number = 4.18\\
Effective reproduction number = 0.59\\
Infection rate\gamma (R-1)＝－1.50e^{-2}

・ Situation in other areas

Kanagawa 1060

As in Hokkaido, Kanagawa Prefecture seems to have passed the peak number of new infections, but it is still around the peak number of infections. The situation is unpredictable. The rate of decrease in the number of new infections is very small, and the number of cures is about to increase.

Basic reproduction number = 4.89\\
Effective reproduction number = 0.63\\
Infection rate\gamma (R-1)＝－1.15e^{-2}

Chiba 823 / Saitama 676

The behaviors of Chiba and Saitama are very similar. As with Kanagawa, both seem to have passed the peak number of new infections. And it is around the peak number of infections.

Basic reproduction number = 5.49\\
Effective reproduction number = 0.06\\
Infection rate\gamma (R-1)＝－3.06e^{-2}

It is uncertain why the number of effective reproductions is larger than that of Chiba. However, Saitama seems to be a little saturated.

Basic reproduction number = 6.78\\
Effective reproduction number = 0.50\\
Infection rate\gamma (R-1)＝－1.08e^{-2}

Ishikawa 260 / Toyama 209

Looking at recent news reports, it is Ishikawa and Toyama that are likely to have a slight increase in infection. As shown below, there are more Ishikawa in the whole, but the behavior is similar. And Ishikawa seems to have reached the peak of the number of new infections after the peak, but Toyama has a small amount, but it is difficult to see if it peaked out because the daily amount continues. By the way.

Basic reproduction number = 5.97\\
Effective reproduction number = 0.47\\
Infection rate\gamma (R-1)＝－1.69e^{-2}

Fitting is very difficult in Toyama, so please use the following as reference information only. The number of effective reproductions is slightly larger.

Basic reproduction number = 5.36\\
Effective reproduction number = 0.81\\
Infection rate\gamma (R-1)＝－9.30e^{-3}

Fukuoka 648, Hyogo 654, Kyoto 328, Aichi 491

In each of these prefectures, the number of new infections has recently decreased to 5 or less. Looking at the graph, the number of infections has started to decrease in Kyoto, where the number of cures has increased, but in other prefectures, the number of cures is still small and the number of infections is waiting to increase in order to decrease. .. However, it seems that the number of cures will surely increase in the future and it will end.

Summary

・ Using the SIHR model, I tried to find the number of effective reproductions in various parts of Japan. ・ In Japan as a whole, the number of infections is about to decrease, and the end is coming to an end. ・ However, Tokyo and Osaka are still on the verge of ending, and it is an urgent task to bring them to an end. Both need to increase the number of cures. ・ Hokkaido is still at the peak of new infections, and the situation is unpredictable. The second challenge is to bring this to an end. -In other areas, the number of new infections has generally turned to a declining trend, and it is thought that the number of infections is near the peak or has entered a period of decline. However, it turns out that the areas covered this time are in an unpredictable situation.

-Since the obtained quantities depend on the input parameters, it is necessary to show the accuracy of the obtained quantities.