**USA**

Day-1 of Exponential Growth Phase | 07 Mar 2020 = Day-1 |

Model Factor (MF) – VARIES | 0.3 to 0.6 |

Point of InfLection based on Real Data best fit ## | 09 Apr 2020 = Day-34 |

Day-15 | 21 Mar 2020 |

DAY-16 | 22 Mar 2020 |

Day-23 | 29 Mar 2020 |

Model Validity with Real Data: Day-1 to Day-15 | VALID for MF=0.30 |

Model Validity with Real Data: Day-16 to Day 23 | VALID for MF=0.6 |

Infections at Day-30 (05 Apr 2020) – PREDICTED* | 532,511 |

Infections on 05 Apr 2020 (Real Measured Data)* | 337,072 |

Infections at Day-45 (20 April 2020) – PREDICTED# | 8,566,413 |

Infections on 20 Apr 2020 (Real Measured Data)* | 784,326 |

* & # Real Measured Data for COVID-19 infections in the US are lower than Predicted Data as per the model for Day-30, by 37%. This is because the model deviates from real world data after 29 Mar 2020. The tested cases are only a subset of the population. Therefore, to obtain the infections in the entire population, we can extrapolate the tested data to the whole population by a multiple.

## InfLection is at Day=40, which falls on 15 Apr 2020. As on this this day the rate of inFection growth has definitely slowed down.

**Italy**

Day-1 of Exponential Growth Phase | 26 Feb 2020 = Day-1 |

Model Factor (MF) | 1.00 |

Point of InfLection based on Real Data best fit ## | 27 Mar 2020 = Day-31 |

Model Validity with Real Data from Day-1 to | 18 Mar 2020 = Day-22 |

Infections at Day-30 (26 Mar 2020) – PREDICTED* | 163,309 |

Infections on 26 Mar 2020 (Real Measured Data)* | 80,589 |

Infections at Day-45 (4 April 2020) – PREDICTED# | 2,627,126 |

Infections on 04 Apr 2020 (Real Measured Data)# | 1,24,632 |

Asymptote based on Real Data – PREDICTED ### | 08 Apr 2020 = Day-43 |

* & # Real Measured Data for COVID-19 infections in Italy are lower than Predicted Data as per the model for Day-30 and Day-45. This is because the model deviates from real world data after 18 Mar 2020. The tested cases are only a subset of the population. Therefore, to obtain the infections in the entire population, we can extrapolate the tested data to the whole population by a multiple.

## InfLection is at Day=31, which falls on 27 Mar 2020. As on this this day the rate of inFection growth has definitely slowed down. Based on this, other countries may also show a slow in growth at about 30 days, provided the steps taken there are similar to the protocols taken in Italy.

### Asymptote is the point where the rate of new InFections drops dramatically, in mathematical terms to zero. However, in the case of real world inFections, the numbers of new inFections would be small compared to the previous days. This is the point when the curve becomes flat.

**UK**

Day-1 of Exponential Growth Phase | 10 Mar 2020 = Day-1 |

Model Factor (MF) | 0.70 |

Point of InfLection based on Real Data best fit ##(Day-37 = 15 Apr 2020 – PREDICTED) | 15 Apr 2020 |

Day-17 | 26 Mar 2020 |

Model Validity with Real Data from Day-1 to Day-17 | VALID |

Infections at Day-30 (08 Apr 2020) – PREDICTED* | 127,495 |

Infections on 08 Apr 2020 (Real Measured Data)* | 60,733 |

Infections at Day-45 (23 April 2020) – PREDICTED# | 2,050,983 |

* & # Real Measured Data for COVID-19 infections in the UK are lower than Predicted Data as per the model for Day-30, by 52%. This is because the model deviates from real world data after 26 Mar 2020. The tested cases are only a subset of the population. Therefore, to obtain the infections in the entire population, we can extrapolate the tested data to the whole population by a multiple.

## InfLection for UK is PREDICTED on 15 Apr 2020 (as per data available on 13 Apr 2020). That’s a total of 37 days from the start of exponential growth.

**France**

Day-1 of Exponential Growth Phase | 05 Mar 2020 = Day-1 |

Model Factor (MF) | 0.80 |

Point of InfLection based on Real Data best fit | 07 Apr 2020 = Day-34 |

Day-21 | 25 Mar 2020 |

Model Validity with Real Data from Day-1 to Day-21 | VALID |

Infections at Day-30 (03 Apr 2020) – PREDICTED* | 140,529 |

Infections on 03 Apr 2020 (Real Measured Data)* | 64,338 |

Infections at Day-45 (18 April 2020) – PREDICTED# | 2,260,661 |

* & # Real Measured Data for COVID-19 infections in France are lower than Predicted Data as per the model for Day-30, by 54%. This is because the model deviates from real world data after 25 Mar 2020. The tested cases are only a subset of the population. Therefore, to obtain the infections in the entire population, we can extrapolate the tested data to the whole population by a multiple.

## InfLection is at Day=34, which falls on 07 Apr 2020. As on this this day the rate of inFection growth has definitely slowed down.

**Spain**

Day-1 of Exponential Growth Phase | 06 Mar 2020 = Day-1 |

Model Factor (MF) | 2.5 |

Point of InfLection based on Real Data best fit ## | 31 Mar 2020 = Day-26 |

Model Validity with Real Data from Day-1 to | 26 Mar 2020 = Day-21 |

Infections at Day-30 (04 Apr 2020) – PREDICTED* | 315,134 |

Infections on 04 Apr 2020 (Real Measured Data)* | 126,168 |

Infections at Day-45 (19 April 2020) – PREDICTED# | 5,069,498 |

* & # Real Measured Data for COVID-19 infections in Spain are lower than Predicted Data as per the model for Day-30, by 60%. This is because the model deviates from real world data after 26 Mar 2020. The tested cases are only a subset of the population. Therefore, to obtain the infections in the entire population, we can extrapolate the tested data to the whole population by a multiple.

## InfLection is at Day=26, which falls on 31 Mar 2020. As on this this day the rate of inFection growth has definitely slowed down.

**Germany**

Day-1 of Exponential Growth Phase | 05 Mar 2020 = Day-1 |

Model Factor (MF) | 0.9 |

Point of InfLection based on Real Data best fit ## | 01 Apr 2020 = Day-28 |

Day-22 | 26 Mar 2020 |

Model Validity with Real Data from Day-1 to | 26 Mar 2020 – Day-22 |

Infections at Day-30 (03 Apr 2020) – PREDICTED* | 202,728 |

Infections on 03 Apr 2020 (Real Measured Data)* | 91,159 |

Infections at Day-45 (19 April 2020) – PREDICTED# | 3,261,248 |

* & # Real Measured Data for COVID-19 infections in Spain are lower than Predicted Data as per the model for Day-30, by 55%. This is because the model deviates from real world data after 26 Mar 2020. The tested cases are only a subset of the population. Therefore, to obtain the infections in the entire population, we can extrapolate the tested data to the whole population by a multiple.

## InfLection is at Day=28, which falls on 01 Apr 2020. As on this this day the rate of inFection growth has definitely slowed down.

**Canada**

Day-1 of Exponential Growth Phase | 16 Mar 2020 = Day-1 |

Model Factor (MF) | 1.25 |

Point of InfLection based on Real Data best fit ## | 08 Apr 2020 = Day-24 |

Day-11 | 26 Mar 2020 |

Model Validity with Real Data from Day-1 to Day-11 | VALID |

Infections at Day-30 (14 Apr 2020) – PREDICTED* | 126,126 |

Infections on 14 Apr 2020 (Real Measured Data)* | NOT YET THERE! |

Infections at Day-45 (29 April 2020) – PREDICTED# | 2,028,971 |

* & # Real Measured Data for COVID-19 infections in Canada will be lower than Predicted Data as per the model for Day-30. This is because the model deviates from real world data after 26 Mar 2020. The tested cases are only a subset of the population. Therefore, to obtain the infections in the entire population, we can extrapolate the tested data to the whole population by a multiple.

## InfLection is at Day=24, which falls on 08 Apr 2020. As on this this day the rate of inFection growth has definitely slowed down. Canada has carried out 8,732 tests/million.

**Australia**

Day-1 of Exponential Growth Phase | 16 Mar 2020 = Day-1 |

Model Factor (MF) | 1.40 |

Point of InfLection based on Real Data best fit ## | 28 Mar 2020 = Day-13 |

Model Validity with Real Data from Day-1 to | 26 Mar 2020 = Day-11 |

Infections at Day-30 (14 Apr 2020) – PREDICTED* | 95,166 |

Infections on 14 Apr 2020 (Real Measured Data)* | NOT YET THERE! |

Infections at Day-45 (29 April 2020) – PREDICTED# | 1,530,911 |

* & # Real Measured Data for COVID-19 infections in Australia will be lower than Predicted Data as per the model for Day-30. This is because the model deviates from real world data after 26 Mar 2020. The tested cases are only a subset of the population. Therefore, to obtain the infections in the entire population, we can extrapolate the tested data to the whole population by a multiple.

## InfLection is at Day=13, which falls on 28 Mar 2020. As on this this day the rate of inFection growth has definitely slowed down. The infLection point for Australia is much faster than for Italy, Spain and Germany.

**China**

Day-1 of Exponential Growth Phase | 22 Jan 2020 = Day-1 |

Model Factor (MF) | 0.1 |

Point of InfLection based on Real Data best fit ## | 12 Feb 2020 = Day-22 |

Model Validity with Real Data from Day-1 to | 10 Feb 2020 = Day-20 |

Infections at Day-30 (20 Feb 2020) – PREDICTED* | 386,705 |

Infections on 20 Feb 2020 (Real Measured Data)* | 75,077 |

Infections at Day-45 (06 Mar 2020) – PREDICTED# | 6,220,851 |

Infections on 06 Mar 2020 (Real Measured Data)# | 80,690 |

Start of Asymptote (Day-46) – Real Data | 07 Mar 2020 |

Current Asymptote Value – Real Data as on 26 Mar 2020 (Day-65) | 81,782 |

* The Day-30 Predicted Data is higher that the Real Measured Data by a factor of 5.

# Day-45 Predicted Data is orders of magnitude than the Real Measured data.

## InfLection is at Day=22, which falls on 02 Feb 2020. As on this this day the rate of inFection growth has definitely slowed down. The infLection point for China is in the same ball park for Italy (Day-30), Spain (Day-27), and Germany (Day-28).

Global estimates of infections as on 26 Mar 2020 was 566,269.

China’s reported infection data for 26 Mar 2020 is 81,792. Out of this, Hubei Province (of which Wuhan is the Capital) has 67,801 reported infections – which is 83% of China’s number. Though infections had spread to 31 other Provinces, they account for only 17% of infections. China’s numbers begin to asymptote around 17 Feb 2020 (Day-27) at reported 72,434 cumulative infections.

China must have been brilliant at curtailing the spread that began the exponential growth phase on 22 Jan 2020, had a point of inflection on 09 Feb 2020 (Day-19) and started the asymptote on 17 Feb 2020 (Day-27). Additionally they supposedly curtailed the spread in other Provinces, but left gaps in the control to spread COVID-19 to 199 Countries and Territories. This very difficult to accept!

Another way to look at it is that China was done with the worst in 27 Days. If you see the country models above, none of the major countries are anywhere near the begin of an asymptote as on 26 Mar 2020 – USA (Day-20), Italy (Day-24), UK (Day-17), France (Day-22), Spain (Day-21), Germany (Day-22), Canada (Day-11), Australia (Day-11).

Finally, China has a population of 1400 million and the above mentioned countries have populations in the range 35 to 65 million. So, we would expect China to have been much worse.

Therfore I will leave the reader to conclude whether we should trust the Prediction or the Real Measured Data for China. My personal opinion is that China’s reported data is a suspect.

**South Korea**

Day-1 of Exponential Growth Phase | 22 Feb 2020 = Day-1 |

Model Factor (MF) | 1.0 |

Point of InfLection based on Real Data best fit ## | 15 Mar 2020 = Day-23 |

Model Validity with Real Data from Day-1 to | 05 Mar 2020 = Day-13 |

Infections at Day-30 (22 Mar 2020) – PREDICTED* | 186,496 |

Infections on 22 Mar 2020 (Real Measured Data)* | 8,961 |

Infections at Day-45 (06 Apr 2020) – PREDICTED# | 3,485,646 |

Infections on 06 Apr 2020 (Real Measured Data)# | NOT YET THERE |

Current Asymptote Value – Real Data as on 26 Mar 2020 (Day-34) | 9,137 |

* The Day-30 Predicted Data and Real Measured Data vary by a huge factor. Since the model is anyway NOT valid beyond Day-13, Predicted Data should be discarded.

# The Predicted Data for Day-45 is a very big number, compared to the Real Measured Data of 9,137 as on 26 Mar 2020. Again, since the model is anyway NOT valid beyond Day-13, Predicted Data should be discarded.

## InfLection is at Day=23, which falls on 15 Mar 2020. As on this this day the rate of inFection growth has definitely slowed down. The infLection point for South Korea is in the same ball park for Italy (Day-30), Spain (Day-27), Germany (Day-28) and China (Day-22).

However, in the case of South Korea, we should probably accept that the Inflection at Day-23 (15 Mar 2020) is real for the very reason that it succeeded in stoping COVID-19 in its tracks. Rather than repeat what is already out there, please see the following article. Further, post Day-23, the curve has begun to asymptote, though not completely reaching a level of zero slope.

South Korea is the only country so far, where the virus was curtailed by targeted lockdowns through the use of technology and the use of best practices via TRACING, TESTING and QUARANTINING. It is also the only country that achieved this without total lockdown.

South Korea is a democratic country. It has a population of about 51 million. It has a testing ratio of 7,502 Tests/Million, which is higher than that for even Italy (6,533 Tests/Million). This data is getting higher and higher each day. Its data and publication methods have been transparent and at par with international norms for reporting.

It is quite evident that South Korea had reached a true point of inflection (second derivate equal to zero) and thereby curtailed COVID-19.

**India**

Day-1 of Exponential Growth Phase | 22 Mar 2020 = Day-1 |

Model Factor (MF) | TBD |

Point of InFlection based on Real Data best fit | NOT YET |

Day-X : End Date for Model Validity | TBD |

Model Validity with Real Data from Day-1 to Day-X | NEED MORE DATA |

Infections at Day-30 (20 Apr 2020) – PREDICTED* | TBD |

Infections on 20 Apr 2020 (Real Measured Data)* | NOT YET THERE! |

Infections at Day-45 (05 May 2020) – PREDICTED# | TBD |

* # The data for India from 22 Mar 2020 to 05 Apr 2020 is spurious. It is far removed from the truth. It is because of insufficient testing in the country. This gives an artificially low number for inFections. The graph, with MF=0.04, is the Italian trend for inFections. The India data is 56% lower than Italy, for the same time period of exponential growth. But, Indian population is 22.56 times the Italian population.

In my previous article I had estimated that 1.44 million people will be infected with COVID-19 by 19 April 2020, but that was based on simple scaling of the Italian Raw Data for population difference between India and Italy.

The quantum of actual testing in India is very low and this may limit the quality of a mathematical model, since the factor MF will not be well known. India is currently doing only 66 Tests/Million people, as on 05 Apr 2020. It is totally inadequate to get the ground level reality. In comparison the testing in other other countries is way higher – 10,896 (Italy); 8,920 (South Korea); 5,421 (US) and 2,895 (UK). This is the reason why it was possible for me to establish a mathematical exponential predictive equation for these countries, but not for India.

As such, until the actual testing data improves in India, it may be difficult to predict the infections for the next 15 to 30 days. The only alternative is to predict the number as reported in my previous article.

**Methodology – Model Equation and Real World Infection Data**

The model has been developed based on the Italian trend for infection spread of COVID-19 (Coronavirus 2019). In a previous article, I had established the equation for the exponential growth model for Italy. This equation was modified for other countries based on a scaling Model Factor (MF) and their population, via a Population Ratio (PR) defined as the “population of a country” divided by “population of Italy”. I’ve used the population data from https://worldpopulationreview.com. In a nutshell the equation takes the form:

Y(t) = MF * PR * 631.06 * exp (0.1852*t)

Y(t) is the “Cumulative Number of Infections” on day “t”. The model equation works in the exponential growth phase for the spread of the virus infection. The start of the exponential growth phase is taken when the cumulative number of infections has reached about 400, based on actual published test raw data, since it works well with the equation for many countries. When this happens, I’ve designated it as Day-1 of the exponential growth phase and t is set to 1 (t=1). For succeeding days, “t” is incremented by one.

I’m comparing the predicted model with the real world data set publicly available from John Hopkins University & Medicine (JHU), Center for Systems Science and Engineering (CSSE). In my view, this is the most reliable data available in a single place for any country.