## Introduction: Estimate the Infection Spread of COVID-19

(Updated: March 21, 23 and 28, 2020. See Step 4 and later.)

Cases of the new corona-virus(COVID-19) infection have been reported in many countries recently. I saw a figure a few days ago. It shows changes in the number of deaths by COVID-19 in 7 countries.

https://www.afpbb.com/articles/-/3274146?pid=2224...

I am a resident in Japan, which is not included in these 7 countries. It has been reported that infection inspection with PCR is limited in Japan in contrast to more active inspection in South Korea or Italy.

[Total COVID-19 tests performed by country by March 20, 2020]

• South Korea: 316,664
• Italy: 206,886
• Germany: 167,000
• Russia: 143,519
• Australia: 113,615
• :
• Japan: 14.901

https://ourworldindata.org/covid-testing

The number of confirmed COVID-19 cases ought to depend on the number of inspection. On the other hand, the number of deaths should far less depend on it. Until an unfortunate death, a few weeks might elapse from infection via positive test result. However we can see the status of outbreaks more precisely in exchange for this time lag. We update the figure above, increasing the number of countries to 10.

## Step 1: Data

OUR WORLD IN DATA provides panel data including the number of Total deaths for the COVID-19 pandemic.

https://ourworldindata.org/coronavirus-source-data

https://covid.ourworldindata.org/data/ecdc/total_...

## Step 2: Figures and Analysis (2020/03/17)

With the downloaded CSV file and M.S. Excel, we can get the figure showing changes in the number of deaths by COVID-19 in many countries.

On March 18, 2020, we drew the first figure. Click and Check a PDF file “covid19.pdf” attached below. We arranged in descending order of the number of deaths and selected worst 10 countries. Then we found the day for each country on which the number of deaths started increasing more than 5 or 6 and we set it as day1.

We can draw the figure in 2 alternative scales; linear and logarithm. For an outbreak with exponential growth, the latter scale is better to see the changing pace. In these 2 figures, China is ahead of the others for a month. Hence we draw additional figures with restricted period; from day1 to day30.

We can know some facts below in these figures.

1. China held down the spread of infection very strongly. However, a little unnatural change of growth is shown in the figure with linear scale at day34 and later. This arresting convergence might be a doubt for credibility of the data(*).
2. In the countries in Europe, the status of outbreaks seems serious. In these countries the rate of increase was not down after day10 different from China.
3. Especially it is very serious in Italy. Even if hereafter the rate of increase will hold down similarly to China, the number of death may reach 100 thousand (30 times as many as in China).
4. South Korea has done the best practice to hold down the spread of infection.
5. Japan and U.S. stand at a critical moment whether they can follow South Korea.
6. The convergence in the countries in Europe will be more than 1 month later, even if they can follow China.

(* Added on March 27, 2020)

Later, we saw an article titled "Report of Urns Stacked at Wuhan Funeral Homes Raises Questions About the Real Coronavirus Death Toll in China" in the TIME.

## Step 3: Alternative Figures

Click and Check a PDF file “covid19_per1M.pdf” attached below. The figures in this file show the changing of number of deaths per 1 million residents in each country.

We can see that the number of deaths has changed in lower level in China and U.S. than the other 8 countries. This contrast might be able to be explained by the deference of concentration of population in urban centers in each country. If so, Japan has done good works in spite of higher concentration of population in urban centers.

## Step 4: Update (2020/03/21)

The data provided by ECDC is updated everyday. Click and Check 2 PDF files “covid19_0322.pdf” and “covid19_0322_per1M.pdf” attached below. The figures in these files were updated 4 days later from the first figures we made in Step 2.

We can know some facts below in these updated figures.

1. In the 5 countries in Europe, the number of deaths has increased 1.6 to 4.4 times for 3 days and reaches 5,767 (1.8 times as many as China).
2. The increasing speed in Italy may seem slightly down in the recent 5 days.
3. Japan seems to be following South Korea.
4. On the other hand, U.S. seems to have sifted to the status with exponential increasing like European countries.
5. In South Korea, a slight sign to fail holding down outbreak may be shown.

## Step 5: Estimation (2020/03/21)

Here we roughly estimate the number of people infected in Japan and U.S.

[Facts]

• Recent total number of deaths: 35(in Japan), 260(in U.S.)
• In South Korea, total number of deaths reached 91 for 14 days after the day when it exceeds 35.
• In Iran, total number of deaths reached 1433 for 14 days after the day when it exceeds 124.

[Assumptions]

1. Period to an unfortunate death after infection: 14 days.
2. 80% persons are subclinical or mild in the cases of positive test results.
3. In all death cases persons are tested and get positive results.
4. Only 5% to 10% persons are tested in the subclinical or mild cases.
5. The rate of deaths in positive test results is 1% to 3%.
6. Japan will follow a path like South Korea.
7. U.S. will follow a path like Iran.

In these assumptions, "2" and "4" are very critical. Though I have seen news that 20% cases reach severe, I don’t know well this ratio is measured in whether just positive test results or whole of infected including un-tested. However if it is measured in the latter, the rate of deaths “1% to 3%” in the assumption "5" above should be assumed in the latter. Then the rate, 1% to 3%, becomes the fatality rate directly. It is much bigger than 0.1% which is the fatality rate in seasonal Influenza. Hence we assume it is measured in the former, and “1% (*)” as the upper estimate of the fatality rate for reference purposes.

[Results of Estimation]

Fatality rate:

• Upper: 1% (* for reference purposes)
• Middle: 3% / (20%+80%/10%) = 0.36%
• Lower: 1% / (20%+80%/5%) = 0.06%

The number of infected in Japan:

• Lower: 91 / 1% = 9100 (*)
• Middle: 91 / 0.36% = 25,000
• Upper: 91 / 0.06% = 150,000

The rate of infection in Japan:

• Lower: 9100 / 126,000,000 = 0.01% (*)
• Middle: 25,000 / 126,000,000 = 0.02%
• Upper: 147,000 / 126,000,000 = 0.12%

The number of infected in U.S.:

• Lower:1433*(260/124) / 1% = 300,000 (*)
• Middle: 1433*(260/124) / 0.36% = 834,000
• Upper: 1433*(260/124) / 0.06% = 5,000,000

The rate of infection in U.S.:

• Lower: 300,000 / 327,000,000 = 0.09% (*)
• Middle: 834,000 / 327,000,000 = 0.25%
• Upper: 5,000,000 / 327,000,000 = 1.5%

Johns Hopkins Coronavirus Resource Center said that the number of the total confirmed cases infected in U.S. was 33,073 at 18:30 on March 22, 2020. Our estimate above is 9 to 151 times as many as this number.

Assume that 4 close contacts to a COVID-19 carrier can make a new infected. And assume the rates of infection are kept. A resident in Japan, who has close contacts to 10 persons everyday randomly, will be infected COVID-19 with 1% to 9% probability after 30 days. And this probability reaches 7% to 68% in U.S..

## Step 6: (2nd Update on 2020/03/23)

We updated figures again 2 days after the first update in Step 4.

Seeing figures in “covid19_per1M_0324.pdf” attached below, we think that medical staff is working hard under the strong strain in Italy, Spain and Iran. And we are worried for France and Netherlands. In Italy and Iran, though the number of deaths has increased about 2 times for 6 days, we can see that the rates of increasing have declined slowly but surely in the figure in logarithm scale. We wish calming down as soon as possible in each country.

## Step 7: (3rd Update on 2020/03/28)

See updated figures in “covid19_0329.pdf ” and “covid19_per1M_0329.pdf” attached below.
The center of the infection has moved to Europe from China. It is serious in Italy and Spain especially. France, U.K. and Netherlands are following the path of Italy 12 to 17 days late.

However the rate of increasing in Italy has declined surely in logarithm scale. On the other hand, the rate is higher in U.S. In U.S. it doesn’t decline in logarithm scale for the latest week.

It seems that Assumption 7 in Step 5 “U.S. will follow a path like Iran,” cannot be supported now. U.S. may follow a path like Spain or more serious. So we change the assumption to “U.S. will follow a path like Italy”. Because the path of Italy is longer than Spain, though it is slower.

The estimate of the number of infected in U.S.:

• Lower: 9136*(1707/1268) / 1% = 1,230,000 (*)
• Middle: 9136*(1707/1268) / 0.36% = 3,420,000
• Upper: 9136*(1707/1268) / 0.06% = 20,500,000

The estimate of the rate of infection in U.S.:

• Lower: 1,230,000 / 327,000,000 = 0.38% (*)
• Middle: 3,420,000 / 327,000,000 = 1.05%
• Upper: 20,500,000 / 327,000,000 = 6.3%

Johns Hopkins Coronavirus Resource Center said that the number of the total confirmed cases infected in U.S. was 124,217 at 10:30 on March 29, 2020. Our estimate above is 10 to 165 times as many as this number.

(* See Step 5 about the Lower estimates.)

[Total Deaths in the worst 30 countries by March 28, 2020]

1. Italy 9,136

2. Spain 4,858

3. China 3,301

4. Iran 2,378

5. France 1,995

6. United States 1,707

7. United Kingdom 759

8. Netherlands 546

9. Germany 325

10. Belgium 289

11. Switzerland 197

12. South Korea 144

13. Argentina 117

14. Brazil 92

15. Sweden 92

16. Turkey 92

17. Indonesia 87

18. Portugal 76

19. Austria 68

20. Philippines 54

22. Denmark 52

23. Japan 49

25. Iraq 40

26. Greece 28

27. Malaysia 26

28. Egypt 24

29. Romania 24

30. Morocco 23