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Corona’s Exponential Curve Slope Tracking, March 20

Summary:
Exponential Growth and Corona The more mathematically versed folks under us have understood that it the slope (or steepness / derivation) of the Corona expansion curve is important. The following statistics is based on the Worldometer data, that rather shows the “first dimension”; we however, focus on the “second dimension”, the slope of the curve. This is far more useful, because for such exponential curve, the slope is key.The video explains the details. [embedded content] Exponential Growth It took the Corona Virus 20 days to grow from 100 to 1000 and 13 days to grow to 1000 to 10000. Attention here: The Y axis has a logarithmic scale. Formulae Exponential Curve ΔNd  is the number of new cases per day. Basic Reproduction Number E is the number of

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Exponential Growth and Corona

The more mathematically versed folks under us have understood that it the slope (or steepness / derivation) of the Corona expansion curve is important.

The following statistics is based on the Worldometer data, that rather shows the “first dimension”; we however, focus on the “second dimension”, the slope of the curve.
This is far more useful, because for such exponential curve, the slope is key.The video explains the details.

Exponential Growth

It took the Corona Virus 20 days to grow from 100 to 1000
and 13 days to grow to 1000 to 10000.

Attention here: The Y axis has a logarithmic scale.

Corona’s Exponential Curve Slope Tracking, March 20

Formulae Exponential Curve

ΔNd  is the number of new cases per day.

Basic Reproduction Number

E is the number of people one person typically infects, the so-called basic reproduction number.
In Wikipedia it is called R0
According to some initial research cited in Wikipedia (e.g. here or here), this number is between 1.4 and 3.9 for Covid19. This would be inferior to the one of SARS, the 2003 outbreak, which had values between 2 and 5.

However this value is highly unprobable, given that SARS only affected 8000 people. Moreover, the high variance of the values are worrying: Minimum 1.4 and maximum 3.9.

Probability for infection 

p is the probability that this infection happens from one person to another.

Key for policy makers is to contain the number of new transmission E*p.
This is mostly done  using measures like

school-closing, social distancing, hand disinfection and lock-downs.

Corona’s Exponential Curve Slope Tracking, March 20

Inflection point from exponential to logistic curve

The second derivation of the formula leads to the inflection point, where the curve converts to a logistic curve.

Reasons are :

  1. E*p gets reduced thanks to the measures above,
    for example from 1.15 to 1.05
  2. Most people cannot be infected anymore because they have had the disease already, the so-called herd immunity. According to the German Robert Koch Institute this can take up to 2 years.

Corona’s Exponential Curve Slope Tracking, March 20

Explanations for the table below

We track average (ΔNd  / N) over 3 days.

ΔNare new cases.

Nd corresponds to the active cases, the ones that may transmit the virus.

When ΔNd  / Nd  is bigger than the previous days, this means that the slope of the curve increases, hence implicitly the growth factor ΔNd  / Nd-1

 

Key Points as of March 20

  • Massive rise in slope in the United State, Germany and Switzerland
  • But also in Brazil, Pakistan and Turkey.

Country
 

Total 

Cases

Latest Period
ΔNd  / NAverage New Cases  in% of Active Cases  per Day
Previous Periods
ΔNd  / Nd
Average New Cases in
% of Active Cases per Day


Curve Trend

Curve Slope Tendency
New Cases
last 3 days
March 18-20
ΔNd  / N
March
15-17

March
12-14
March
08-11
March
04-07
Total World 275,557 77379 34% 18% 19% 11% 8% Double in 2-3 days Rising vs (nearly) all periods
China 80,967 86 0.24% 0.16% 0.07% 0.16% 0.42% Flat or Flattening Flat or Near Flat
Italy 47,021 15,515 29% 19% 27% 32% 37% Double in 4 to 5 days Slope Mostly Rising
Spain 21,571   9,745 57% 32% 67% 96% 52% Double in less than 2 days Slope Rising Again After Slowing
Germany 19,848 10,481 77% 35% 48% 35% 84% Double in less than 2 days Rising vs nearly all periods
Iran 19,644  3,475 15% 15% 22% 20% 48% Double in 5 to 10 days Only Recently Rising
USA 19,383 12,944 158% 44% 41% 54% 79% Double in less than 2 days Rising vs nearly all periods
France 12,612 4,882 37% 25% 33% 36% 94% Double in 2-3 days Rising vs nearly all periods
S. Korea 8,652   332 2% 1% 1% 3% 92% Flat or Flattening Flat or Near Flat
Switzerland 5,615 2,873 71% 34% 37% 36% 94% Double in less than 2 days Rising vs nearly all periods
UK 3,983 2,033 62% 25% 53% 76% 92% Double in less than 2 days Slope Mostly Rising
Netherlands 2,994 1,289 45% 26% 31% 42% 179% Double in 2-3 days Rising vs nearly all periods
Austria 2,649 1,317 68% 35% 56% 52% 59% Double in less than 2 days Rising vs nearly all periods
Belgium 2,257 1,014 49% 27% 40% 22% 325% Double in 2-3 days Rising vs nearly all periods
Norway 1,959 489 15% 11% 25% 76% 93% Double in 5 to 10 days Slope Rising Again After Slowing
Sweden 1,639 443 15% 8% 31% 53% 113% Double in 5 to 10 days Slope Rising Again After Slowing
Denmark 1,255 278 11% 6% 20% 468% 43% Double in 5 to 10 days Only Recently Rising
Canada 1,087 489 69% 50% 46% 24% 33% Double in less than 2 days Rising vs all periods
Malaysia 1,030 357 59% 71% 24% 20% 102% Double in less than 2 days Slope Falling or Constant
Portugal 1,020 572 114% 56% 62% 45% 106% Double in less than 2 days Rising vs nearly all periods
Japan 1,007 129 7% 4% 11% 12% 17% Double in 10 – 15 days Only Recently Rising
Brazil 970 624 139% 43% 63% 43% 213% Double in less than 2 days Rising vs nearly all periods
Australia 928 476 73% 31% 40% 26% 39% Double in less than 2 days Rising vs nearly all periods
Czechia 833 399 70% 43% 34% 65% 105% Double in less than 2 days Rising vs nearly all periods
Diamond 

Princess

712 16 2% 0% 0% 0% 0% Flat or Flattening Rising vs nearly all periods
Israel 705 368 65% 25% 34% 82% 30% Double in less than 2 days Slope Mostly Rising
Ireland 683 391 103% 43% 68% 32% 213% Double in less than 2 days Rising vs nearly all periods
Turkey 670 572 3178% 511% 167% New New Double in less than 2 days Slope Mostly Rising
Pakistan 501 254 292% 248% 24% 65% 5% Double in less than 2 days Rising vs (nearly) all periods
Greece 495 108 17% 24% 43% 13% 211% Double in 5 to 10 days Slope Falling or Constant
Luxembourg 484 344 229% 59% 210% 33% 50% Double in less than 2 days Rising vs (nearly) all periods
Qatar 470 28 3% 11% 10% 521% 13% Flat or Flattening Slope Falling or Constant
Finland 450 128 20% 15% 95% 56% 50% Double in 5 to 10 days Only Recently Rising
Chile 434 233 127% 77% 55% 90% 100% Double in less than 2 days Rising vs (nearly) all periods
Ecuador 426 315 389% 102% 22% 5% 25% Double in less than 2 days Rising vs (nearly) all periods
Poland 425 187 72% 52% 77% 104% New Double in less than 2 days Only Recently Rising
Iceland 409 162 34% 18% 30% 18% 98% Double in 2-3 days Rising vs (nearly) all periods
Singapore 385 119 37% 17% 14% 21% 22% Double in 2-3 days Rising vs (nearly) all periods
Indonesia 369 197 79% 31% 67% 188% 25% Double in less than 2 days Slope Mostly Rising
Saudi Arabia 344 173 57% 22% 44% 158% 150% Double in less than 2 days Slope Mostly Rising
Slovenia 341 66 12% 17% 73% 94% New Double in 5 to 10 days Slope Falling or Constant
Thailand 322 145 105% 69% 32% 13% 15% Double in less than 2 days Rising vs (nearly) all periods
Romania 308 91 27% 27% 62% 85% 75% Double in 4 to 5 days Slope Falling or Constant
Bahrain 298 57 13% 6% 4% 35% 18% Double in 5 to 10 days Slope Mostly Rising
Egypt 285 89 37% 36% 51% 6% 1150% Double in 2-3 days Slope Falling or Constant
Estonia 283 58 17% 32% 206% 15% 100% Double in 5 to 10 days Slope Falling or Constant
Peru 263 146 128% 69% 64% 29% 2% Double in less than 2 days Rising vs (nearly) all periods
Hong Kong 256 88 51% 15% 8% 8% 3% Double in less than 2 days Rising vs (nearly) all periods
Russia 253 139 91% 36% 76% 10% 300% Double in less than 2 days Rising vs (nearly) all periods
India 249 106 42% 18% 20% 23% 233% Double in 2-3 days Rising vs (nearly) all periods
Philippines 230 43 14% 25% 46% 358% New Double in 5 to 10 days Slope Falling or Constant
Iraq 208 54 24% 20% 27% 9% 17% Double in 4 to 5 days Slope Falling or Constant
South Africa 202 117 103% 41% 64% 138% New Double in less than 2 days Slope Mostly Rising
Panama 200 131 125% 31% 133% New New Double in less than 2 days Only Recently Rising
Lebanon 177 53 20% 12% 18% 31% 29% Double in 5 to 10 days Slope Mostly Rising
Mexico 164 82 124% 85% 150% 10% 0% Double in less than 2 days Slope Falling or Constant
Kuwait 159 29 10% 9% 15% 5% 2% Double in 10 – 15 days Slope Falling or Constant
Argentina 158 79 61% 26% 48% 31% 200% Double in less than 2 days Rising vs (nearly) all periods
San Marino 151 32 12% 7% 22% 44% 36% Double in 5 to 10 days Only Recently Rising
Colombia 145 80 121% 65% 48% 200% New Double in less than 2 days Slope Mostly Rising
UAE 140 27 14% 14% 6% 19% New Double in 5 to 10 days Slope Falling or Constant
Slovakia 137 40 30% 40% 113% 58% New Double in 2-3 days Slope Falling or Constant
Armenia 136 58 107% 111% 567% 0% 0% Double in less than 2 days Slope Falling or Constant
Serbia 135 63 46% 19% 94% 275% New Double in 2-3 days Only Recently Rising
Taiwan 135 58 60% 25% 6% 3% 3% Double in less than 2 days Rising vs (nearly) all periods
Croatia 130 61 55% 27% 35% 15% 8% Double in less than 2 days Rising vs (nearly) all periods
Bulgaria 127 46 39% 34% 189% 63% New Double in 2-3 days Only Recently Rising
Costa Rica 113 63 78% 46% 36% 300% New Double in less than 2 days Slope Mostly Rising
Latvia 111 51 68% 45% 59% New 0% Double in less than 2 days Slope Mostly Rising
Uruguay 110 81 675% 208% New New New Double in less than 2 days Only Recently Rising
Algeria 94 33 46% 33% 28% 1% 34% Double in 2-3 days Rising vs (nearly) all periods
Vietnam 91 25 23% 12% 23% 113% New Double in 4 to 5 days Only Recently Rising
Bosnia  89 55 87% 21% 67% 33% New Double in less than 2 days Rising vs (nearly) all periods
Morocco 86 42 88% 54% 80% 50% 25% Double in less than 2 days Rising vs (nearly) all periods
Hungary 85 35 40% 23% 44% 40% New Double in 2-3 days Slope Falling or Constant
Jordan 85 37 New New 0% 0% 25% Double in less than 2 days Slope Falling or Constant
Faeroe Islands 80 33 122% 141% 117% 0% New Double in less than 2 days Slope Falling or Constant
Brunei 78 22 18% 13% 88% New New Double in 5 to 10 days Only Recently Rising
North
Macedonia
76 45 125% 50% 29% 33% 50% Double in less than 2 days Rising vs (nearly) all periods
Andorra 75 36 1200% 1267% 0% 0% 0% Double in less than 2 days Slope Falling or Constant
Cyprus 75 26 33% 29% 111% New New Double in 2-3 days Only Recently Rising
Sri Lanka 73 29 107% 126% 267% New New Double in less than 2 days Slope Falling or Constant
Dominican
Republic
72 51 155% 30% 40% 38% 25% Double in less than 2 days Rising vs (nearly) all periods
Albania 70 15 14% 15% 55% New New Double in 5 to 10 days Slope Falling or Constant
Belarus 69 33 46% 13% 100% 13% 125% Double in 2-3 days Slope Falling or Constant
Lithuania 69 43 179% 71% 67% 50% 0% Double in less than 2 days Rising vs (nearly) all periods
Moldova 66 36 100% 50% 100% 50% New Double in less than 2 days Slope Falling or Constant
Venezuela 65 32 533% 517% New New New Double in less than 2 days Only Recently Rising
Malta 64 26 51% 39% 67% 25% New Double in less than 2 days Slope Falling or Constant
Tunisia 54 29 54% 13% 52% 150% 0% Double in less than 2 days Slope Mostly Rising
Kazakhstan 52 19 106% 150% New New New Double in less than 2 days Slope Falling or Constant
New Zealand 52 40 190% 24% 13% 0% 100% Double in less than 2 days Rising vs (nearly) all periods
Cambodia 51 18 100% 144% 67% 25% New Double in less than 2 days Slope Falling or Constant
Guadeloupe 51 45 500% 33% New New New Double in less than 2 days Only Recently Rising
Oman 48 15 50% 47% 4% 4% 10% Double in 2-3 days Rising vs (nearly) all periods
Palestine 48 7 6% 3% 9% 14% New Double in 10 – 15 days Only Recently Rising
Senegal 47 20 35% 11% 189% 0% 25% Double in 2-3 days Slope Falling or Constant
Azerbaijan 44 10 30% 58% 17% 6% 50% Double in 2-3 days Slope Falling or Constant
Georgia 44 10 11% 4% 8% 21% 83% Double in 5 to 10 days Slope Mostly Rising
Ukraine 41 27 450% 183% 67% 0% 0% Double in less than 2 days Rising vs (nearly) all periods
Burkina Faso 40 25 417% 217% 0% New New Double in less than 2 days Slope Mostly Rising
R茅union 38 29 161% 17% 167% New New Double in less than 2 days Only Recently Rising
Uzbekistan 33 22 New New New New New Double in less than 2 days Slope Falling or Constant
Martinique 32 17 57% 17% 78% New New Double in less than 2 days Only Recently Rising
Liechtenstein 28 9 75% 125% 100% 0% 0% Double in less than 2 days Slope Falling or Constant
Cameroon 27 17 283% 133% 0% 0% New Double in less than 2 days Rising vs (nearly) all periods
Afghanistan 24 2 6% 33% 19% 19% New Double in 10 – 15 days Slope Falling or Constant
Honduras 24 16 178% 56% 17% New New Double in less than 2 days Slope Mostly Rising
Cuba 21 16 133% 8% New New New Double in less than 2 days Only Recently Rising
Bangladesh 20 10 111% 56% 22% New New Double in less than 2 days Slope Mostly Rising
Jamaica 19 7 29% 17% 100% New New Double in 4 to 5 days Only Recently Rising
DRC 18 15 250% 17% 33% New New Double in less than 2 days Slope Mostly Rising
Paraguay 18 9 43% 10% 13% 100% New Double in 2-3 days Slope Mostly Rising
Macao 17 4 New New New New 0% Double in less than 2 days Slope Falling or Constant
Rwanda 17 10 333% 200% New New New Double in less than 2 days Only Recently Rising
Bolivia 16 4 13% 7% 133% New New Double in 5 to 10 days Only Recently Rising
Ghana 16 9 150% 83% New New New Double in less than 2 days Only Recently Rising
French Guiana 15 4 19% 19% 13% New New Double in 5 to 10 days Slope Falling or Constant
Guyana 15 8 New New New New New Double in less than 2 days Slope Falling or Constant
Guam 14 9 New New New New New Double in less than 2 days Slope Falling or Constant
Montenegro 14 12 New New New New New Double in less than 2 days Slope Falling or Constant
Puerto Rico 14 9 100% 22% New New New Double in less than 2 days Only Recently Rising
Maldives 13 0 0% 10% 8% 75% New Flat or Flattening Flat or Near Flat
Channel Islands 12 6 67% 33% 17% New New Double in less than 2 days Slope Mostly Rising
Guatemala 12 4 133% 233% New New New Double in less than 2 days Slope Falling or Constant
Mauritius 12 12 New New New New New Double in less than 2 days Slope Falling or Constant
Nigeria 12 9 150% 17% 0% 25% 0% Double in less than 2 days Rising vs (nearly) all periods
French
Polynesia
11 8 89% 0% New New New Double in less than 2 days Only Recently Rising
Monaco 11 2 33% 117% 33% 0% 0% Double in 2-3 days Slope Falling or Constant
Gibraltar 10 7 New New New 0% New Double in less than 2 days Slope Falling or Constant
Ethiopia 9 3 100% 167% New New New Double in less than 2 days Slope Falling or Constant
Ivory Coast 9 5 167% 100% 0% New New Double in less than 2 days Slope Mostly Rising
Togo 9 8 267% 0% 0% 0% New Double in less than 2 days Rising vs (nearly) all periods
Trinidad
and Tobago
9 4 67% 50% New New New Double in less than 2 days Only Recently Rising
Kenya 7 3 100% 133% New New New Double in less than 2 days Slope Falling or Constant
Mayotte 7 4 133% 67% New New New Double in less than 2 days Only Recently Rising
Seychelles 7 3 50% 33% New New New Double in 2-3 days Only Recently Rising
Barbados 6 4 New New New New New Double in less than 2 days Slope Falling or Constant
Equatorial
Guinea
6 5 New New New New New Double in less than 2 days Slope Falling or Constant
Kyrgyzstan 6 6 New New New New New Double in less than 2 days Slope Falling or Constant
Mongolia 6 1 33% 133% 0% New New Double in 2-3 days Slope Falling or Constant
Tanzania 6 5 New New New New New Double in less than 2 days Slope Falling or Constant
Aruba 5 2 33% 17% New New New Double in 2-3 days Only Recently Rising
Bahamas 4 3 New New New New New Double in less than 2 days Slope Falling or Constant
Gabon 4 3 100% 0% New New New Double in less than 2 days Only Recently Rising
Saint Martin 4 2 33% 0% 0% New New Double in 2-3 days Slope Mostly Rising
Suriname 4 3 100% 0% New New New Double in less than 2 days Only Recently Rising
CAR 3 2 New New New New New Double in less than 2 days Slope Falling or Constant
Cayman Islands 3 2 67% 0% New New New Double in less than 2 days Only Recently Rising
Congo 3 2 New New New New New Double in less than 2 days Slope Falling or Constant
Curacao 3 3 New New New New New Double in less than 2 days Slope Falling or Constant
Madagascar 3 3 New New New New New Double in less than 2 days Slope Falling or Constant
Namibia 3 1 17% 0% New New New Double in 5 to 10 days Only Recently Rising
St. Barth 3 0 0% 67% 0% New New Flat or Flattening Flat or Near Flat
U.S. Virgin Islands 3 1 33% 33% New New New Double in 2-3 days Slope Falling or Constant
Benin 2 1 New New New New New Double in less than 2 days Slope Falling or Constant
Bermuda 2 2 New New New New New Double in less than 2 days Slope Falling or Constant
Bhutan 2 1 33% 0% 0% 0% New Double in 2-3 days Rising vs (nearly) all periods
Greenland 2 1 New New New New New Double in less than 2 days Slope Falling or Constant
Guinea 2 1 33% 0% New New New Double in 2-3 days Only Recently Rising
Haiti 2 2 New New New New New Double in less than 2 days Slope Falling or Constant
Isle of Man 2 2 New New New New New Double in less than 2 days Slope Falling or Constant
Liberia 2 0 New New New New New Double in less than 2 days Slope Falling or Constant
Mauritania 2 1 33% 0% New New New Double in 2-3 days Only Recently Rising
New Caledonia 2 2 New New New New New Double in less than 2 days Slope Falling or Constant
Nicaragua 2 2 New New New New New Double in less than 2 days Slope Falling or Constant
Saint Lucia 2 0 0% 33% New New New Flat or Flattening Flat or Near Flat
Sudan 2 1 New New New New New Double in less than 2 days Slope Falling or Constant
Zambia 2 2 New New New New New Double in less than 2 days Slope Falling or Constant
Angola 1 1 New New New New New Double in less than 2 days Slope Falling or Constant
Antigua
and Barbuda
1 0 0% 0% New New New Flat or Flattening Flat or Near Flat
Cabo Verde 1 1 New New New New New Double in less than 2 days Slope Falling or Constant
Chad 1 1 New New New New New Double in less than 2 days Slope Falling or Constant
Djibouti 1 1 New New New New New Double in less than 2 days Slope Falling or Constant
El Salvador 1 1 New New New New New Double in less than 2 days Slope Falling or Constant
Eswatini 1 0 0% 0% New New New Flat or Flattening Flat or Near Flat
Fiji 1 1 New New New New New Double in less than 2 days Slope Falling or Constant
Gambia 1 0 New New New New New Double in less than 2 days Slope Falling or Constant
Montserrat 1 1 New New New New New Double in less than 2 days Slope Falling or Constant
Nepal 1 0 New New New New New Double in less than 2 days Slope Falling or Constant
Niger 1 1 New New New New New Double in less than 2 days Slope Falling or Constant
Papua
New Guinea
1 1 New New New New New Double in less than 2 days Slope Falling or Constant
Sint Maarten 1 1 New New New New New Double in less than 2 days Slope Falling or Constant
Somalia 1 0 New New New New New Double in less than 2 days Slope Falling or Constant
St. Vincent
Grenadines
1 0 0% 0% New New New Flat or Flattening Flat or Near Flat
Vatican City 1 0 0% 0% 0% 0% New Flat or Flattening Flat or Near Flat
Zimbabwe 1 1 New New New New New Double in less than 2 days Slope Falling or Constant
Total: 275,557 77379 34% 18% 19% 11% 8% Double in 2-3 days Rising vs (nearly) all periods

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George Dorgan
George Dorgan (penname) predicted the end of the EUR/CHF peg at the CFA Society and at many occasions on SeekingAlpha.com and on this blog. Several Swiss and international financial advisors support the site. These firms aim to deliver independent advice from the often misleading mainstream of banks and asset managers. George is FinTech entrepreneur, financial author and alternative economist. He speak seven languages fluently.

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