[SIR model analysis] Peak out of infection numbers in Japan and around the world ♬ Part 2

Last time, the number of infections began to peak in Europe and the United States to some extent, but let's see what happened after a week. And above all, Japan, where the state of emergency was expanded nationwide from yesterday, had just entered the expansion period a week ago, and about a week has passed, but how has that changed in the past week? I will see it. This time too, the calculation is based on the SIR model and is calculated by an amateur ・ Interpretation. Please make your own judgment at your own risk. In addition, the data was used from the following site as in the previous article. For Japanese data, cases read and use ② below. [Data acquisition] ①COVID-19/csse_covid_19_data/csse_covid_19_time_series (2) New coronavirus seen in data and graphs @ NTV NEWS

What i did

・ Situation in Japan ・ World and US situation ・ Europe situation ・ The situation in China and South Korea that should have ended

・ Situation in Japan

Finally, today, April 18th, the number of infected people has exceeded 10,000. The graph below shows the data up to 4/17 yesterday. Feature (1) Red plot; The number of infections increased exponentially, but it can be seen that the slope decreased from 7 days ago. Since the graph is on the 9th day after the state of emergency was declared in 7 prefectures, there is a guideline of 2 weeks if there is a strong effect, so I would like to expect a significant decrease in the number of infections in the next few days. In addition, since the extension line has fallen asleep, it can be predicted that the number of existing infections will not reach the level of 100,000 as it is, and 20,000 will be about two weeks away, so it can be said that it depends on the effect of the measures.

【reference】 ・ "Emergency Declaration" comes into effect in 7 prefectures New Corona @ April 8, 2020 0:03 (3) Green plot: The number of cures + the number of deaths, but it has not increased much. Although it is increasing exponentially, it is expected to increase further from around today because it has reached the same level 20 days behind the number of infections. (3) Black plot; Number of existing infections / (Number of cures + Number of deaths) (1) It seems that the plot becomes saturated and starts to decrease as the slope of the plot becomes smaller. The number of patients at medical institutions is the number of existing infections, but if this decreases further, it can be expected that the number of patients at medical institutions will gradually decrease (as an index, the downward trend can be seen first).

In the graph above, the vertical axis is the infection rate $ \ gamma (R-1) $, and I was finally sleeping last time, but this value has decreased. That is, it means that the rate of producing infected persons per patient has decreased. Since it is around 0.07 now, if there are 100 patients, it can be seen that 7 infected people are born the next day. ** Since the number of existing infections yesterday is 8710, the number of infections today is 609, but since it is actually 583 (from reference 2 above), it can be said that this infection rate is on a downward trend. ** ** By the way, if this is continued, the prediction can be calculated, but the transmission of infectious diseases is meaningless because the coefficient of the differential equation changes greatly depending on the measure, and it seems better to treat it as a simple relational expression.

・ World and US situation

・ World situation

The increasing trend of the world has also fallen asleep. So I don't think there are up to 10 million infected people. However, the negative slope of the infection rate $ \ gamma (R-1) $ has become smaller. This indicates that the infection does not end and may last for a long time. This is a similar phenomenon in each country that will appear later, and there is a tendency that the infection rate does not decrease easily from 0.05 or less.

・ Situation in the United States

The United States is likely to have a closer peak of infections than the rest of the world, and the red plot has fallen asleep. However, 1 million people are on the verge of a logarithmic graph, and it is likely to reach it in about two weeks. I think we need to take further measures to prevent this. The number of cures in the United States tends to be too low. Due to the explosive expansion, the number of healing days was originally about 20 days, and it is expected that the number of healings will increase from now on, but this number of days seems to be increasing slightly. The problem is the tendency of the graph below. That is, the infection rate $ \ gamma (R-1) $ did not drop from 0.05 and turned sideways. There has been a tendency for the decline to slow down on Saturdays and Sundays, so I hope it will decline after this. Even so, the inclination seems to be small.

・ Europe situation

It was said that the peak of infection was about to be seen in each European country last time. Exit strategies were announced in many countries yesterday, but what about the situation a week later?

·Germany

It is one of the best countries. Clearly, it has crossed the peak number of infections, crossed the cure number curve, and is about to end. Furthermore, looking at the black plot, it is steadily decreasing, falling below 1 and ranking 0.8, so it can be assumed that the number of patients at medical institutions is also decreasing. However, the extrapolated straight line of the latest plot is pointing upwards. This means that the infection has not stopped. This is the blue plot in the figure below; the effective reproduction number R_est is parallel (about 1.5) just before 1, and if this is not 1 or less, the infection will not stop and it will take a long time.

·Switzerland

Switzerland seems to be better than Germany. The peak number of infections has been exceeded, the number of cures curves has crossed, and the number of existing infections has dropped below 10,000, and it seems that medical institutions are getting more room. However, even in Switzerland, the infection rate did not reach zero and became parallel in the last few days. The situation is still unpredictable.

·Spain

Spain worried about medical collapse is as follows Actually, it seems that the number of infections has peaked, but it has not decreased, and it may have started to increase in the last few days. And the number of cures is likely to cross soon, but it cannot. Even in the black plot, this tendency seems to turn to a slight increase just before 1. It can be said that the situation is unpredictable. In Spain, as in Switzerland, the infection rate has turned to an increasing trend. It's unclear what's going on, but it seems to be a very important step here to tighten and contain.

·Italy

Last time, Italy was in a situation where the peak number of infections was likely to be seen. However, it has not decreased since then and has not peaked. This seems to be due to the fact that the number of days until healing has increased to 20 days or more on the way compared to other countries. Still, the number of cures is steadily increasing, so it looks like it will steadily end. Even so, the black plot is still large, and the cumulative number of deaths has exceeded 20,000, so the collapse of medical care is a concern. The graph of infection rate below also has a small slope, indicating that infection is still continuing, and the situation is unpredictable.

·France

In France, the data is rough, so it is not clear yet, but it seems that the number of infections curve and the number of cures (+ deaths) curve are almost the same. However, since the cumulative number of deaths is large and the number of cures is still small, it must be said that the situation is dangerous. Also, the black plot was steadily decreasing, but it seems that it has increased significantly and stopped decreasing after coming here. It can be said that the situation is unpredictable. Since the data is a few rough, I can't draw a picture with a beautiful infection rate. However, looking at the figure below, it can be said that the overall end is nearing, and the infection rate has decreased to about 0.2. Still, it can be said that the situation is unpredictable.

・ UK

Since there is no data on the number of cures, there is no help for it, but at least the peak number of infections is still in the graph. Looking at the following, it seems that it will take at least two weeks.

・ The situation in China and South Korea that should have ended

・ Wuhan

Wuhan is the epicenter of the infection, but it is almost over now. The situation is as follows. Even so, after about 50 days, about 100 infected people still remain. It seems that the day when it becomes 0 is still far away. Since the infection rate continues to be 0.01 or less, the expected value will be 0 or less if the number of infected people is 100 or less. It can be said that it has ended in that sense.

·Korea

On the other hand, South Korea has at least passed the peak number of infections, and the number of cures has increased sufficiently. However, the decrease in Wuhan seems to be convex downward when compared to the function being convex upward. In other words, the number of infections is decreasing very slowly, and it is predicted that it will be prolonged if it is left as it is. This can also be seen from the infection rate graph below. In other words, the infection rate of about 0.02 remains even after the end, and it seems that it will remain without much decrease even after 2 weeks. In other words, if there are about 2000 existing infected people, about 40 people will be reproduced every day. In order to end the infection, some people will be infected unless this value becomes 0.

·Taiwan

The number of infections has exceeded the peak, and the number of cures is increasing, which seems to be going well. However, looking at the figure below, the infection rate has just been suppressed today, and the situation is still unpredictable.

·Hong Kong

Hong Kong is coming in much the same way as Taiwan. The transition of the infection rate seems to have come to an end here.

・ Other countries of concern

·India

Last time it was hopeless during the expansion period, but in the past week, the end has begun to appear. In particular, the number of infections is likely to slow down a little and peak in the future. Furthermore, the infection rate has fallen below 0.1. I hope it will decrease steadily.

·Thailand

At the beginning of the outbreak, Thailand was as common in Asia as Japan. However, it can be said that the effect of the strict measures of the Minister of Health has exceeded the peak number of infections, crossed the curve of the number of cures, and is approaching the end. However, even here, the infection rate does not become 0 obediently, but becomes parallel around 0.25. In other words, it can be said that the infection has not subsided yet and it is a dangerous situation.

·Russia

I was doing it on TV tonight when it was a difficult situation, so I calculated it. It is as follows. It is still in the expansion period and has already exceeded 30,000 people. This is worse than India and is likely to be on par with Europe. As a prediction, it is likely to reach about 100,000 people in two weeks. On the other hand, the infection rate is as follows. The infection rate is still high at 0.15, and the direction of termination is unknown. As a rough estimate, the infection rate is currently increasing by about 5,000 people a day.

・ Discussion

Overall, it is nearing its end, but it seems that it will be necessary to continue implementing non-contact measures for a considerable amount of time before it reaches a complete end. In particular, what is the cause of the phenomenon that the infection rate leveled off and did not reach 0 just before the end, as seen recently in Europe, the United States and Thailand? It is thought that the world will not end unless it is overcome here. Japan also seems to be making incomparable improvements compared to a week ago, but it seems that another breath of patience is needed. By the way, the number of infections in Japan today is 583, which is lower than the predicted 609, and the infection rate can be expected to decrease.

Summary

・ Since the state of emergency has been expanded nationwide and one week has passed since the last time, we have an overview of the world situation. ・ Infections have exceeded the peak of infectious diseases in Europe, the United States and Asia, and can be expected to end in the future. ・ On the other hand, looking at Wuhan and South Korea, it seems that it will take more than three months even after starting to end. ・ Japan is finally beginning to take effect, and an exit strategy may be shown in a week.

・ Let's think about the solution when the parameters of the differential equation move. (Sequential self-consistent solution ... ??)

・ The code is placed below

・ Collive_particles / fitting_gamma_R_II.py