It is my intent to update the above graph for India from 22 Mar 2020 to 22 Apr 2020. The graph above will be replaced on a daily basis. In the above graph t=1 is Day-1 which is set at 22 Mar 2020. Like wise t=2 and so on will increment from the set point date of 22 Mar 2020. For those who don’t like math, they just have to look at the graph and see the trends.
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, the Indian population is 22.56 times that of the Italian population.
The model has close likeness for MF = 0.02, which means that it is following a curve trend that has values lower than that for Italy. Further, we should be expecting an MF = 1, since India should scale to Italy based on the Population Ratio (PR). So, an MF = 0.02 is unreliable and should not be used as a possible model.
The real time data for the exponential growth phase for infections had started on 22 Mar 2020. However, as seen from the graph, the real data does not fit the model, for any value of practical MF. As such, it is very likely that the Real Data published for India by JHU is not of practical use and also does not represent a good sample of the population.
A key conclusion that can be made as on 05 Apr 2020 is that the reported data for inFections in India is totally wrong, in its entirety.
In my previous article, I had established the equation for the exponential growth model for Italy. The population ratio (PR) is 22.56673 for India. Multiplying the exponential growth model with PR should take into account the population differences. I’ve further multiplied it with a Model Factor (MF), which is a number greater than 0, but more likely about 1 for India. This factor fine tunes the scaling and at some value it will have a good match to the real world infection data. When MF is 1/PR, the curve is an identical match to the exponential best fit for Italy.
As such, for India, the modified exponential equation is:
y(t) = MF * PR * 631.06 * exp (0.1852*t)
y(t) = MF * 22.56673 * 631.06 * exp (0.1852*t)
To predict the Infection Cases in India, select an MF between 0 and 1, plug in a value of “t”, where “t” is the day count starting from 22 Mar 2020 (t=1) for India. The computed value of y(t) is the predicted Infection Cases on day “t”.
Days (Scaled to match exponential infection growth trend in Italy)
Let me summarize first and then I’ll explain the model next.
By the third week of April (most likely around 19 April 2020) the model predicts COVID-19 (Coronavirus 2019) infections in India at 1.44 million and deaths due to COVID-19 at 137,000.
The death rate in India should plateau off earliest by 20 May 2020 or latest by 20 July 2020, provided we follow the lockdown and medical protocols used in Italy, France and the US, and possibly China.
I hope I’m terribly wrong and that the actual data will be much lower. But, my analysis comes out of a simple mathematical model, which has been done by scaling and population normalization on the data set publicly available from John Hopkins University & Medicine, Center for Systems Science and Engineering (CSSE). The data set is available here. The time wise data in the set is based on the cumulative number of infections and deaths.
The John Hopkins raw data is available for almost all the countries where COVID-19 has spread. I’ve analyzed the data for a small sub-set of countries – China, France, US, Italy and India, since my primary goal was to figure out some predictions for India.
COVID-19 Infection Analysis
Below is the graph for the confirmed infections in these countries.
This graph shows that the data for China pretty much starts from the exponential growth phase for the infections. We just don’t have any reliable data prior to 22 Jan 2020.
The first documented infections reported in the data set are 2 for France on 24 Jan 2020, 1 for US on 22 Jan 2020, 2 for Italy on 31 Jan 2020 and 1 for India on 31 Jan 2020.
The exponential growth starts at about 05 Mar 2020 for France (380 cases), 07 Mar 2020 for US (402 cases), 26 Feb 2020 for Italy (453 cases) and 22 Mar 2020 for India (396 cases).
To visualize the country trends during the exponential growth rate regime, I have rescaled the data, by simply shifting the origin. I’ve taken Day-1 as 22 Jan 2020 for China, 05 Mar 2020 for France, 07 Mar 2020 for US, 26 Feb 2020 for Italy and 22 Mar 2020 for India. The results are quite interesting.
Days (Scaled to match exponential infection growth trend in Italy)
In the scaled data the trends for these five countries are very similar in the first 6 days. China data deviates from day 6 and the US data deviates from day 12. The data for Italy and France are almost identical. India is just starting on the curve at Day-1 and Day-2.
The trends can be explained on the ability of the countries to carry out testing for COVID-19 and also the population density. China having a population of 1434 million explodes off after Day-6 and the US with a population of 329 million branches off dramatically at Day-12. Notice how close the trend is for France and Italy with populations of 65 million and 60 million respectively. The COVID-19 growth patterns in these two countries are so identical. Considering that these two countries have a similar and robust health care system and testing system, we should be able to trust the data and categorize it as reliable.
It’s challenging to say what is happening in India. The first reported case was on 31 Jan 2020. It’s taken until 22 Mar 2020 to reach the start of the exponential growth stage at an infection level of 396. It’s impossible to have such a long gestation period. Either India is very lucky up to now or the data is completely wrong. It’s likely that the raw data is wrong, since the country may have missed out on enhanced testing during this period. My personal experience has been that the Private Health Care in India is at par with the rest of the world, in many cases better than the US and Europe. However, the concern is the quality of health care that can be given to the poor and underprivileged. Its tough for this category of population. The care needed for a COVID-19 infection is almost impossible to administer for this group.
If we were to model the trend based on one reference country, which one would it be? I would go with the Italian data set for several reasons. First, it models well with the data from France, both having similar population. Second, the Day-1 start of 22 Feb 2020 for Italy is much earlier than the Day-1 start of 05 Mar 2020 for France, and we have more predictive data to work with. Third, the US was not testing enthusiastically in the early days and it is only just about catching up. Italy had a better record of testing than the US and it’s Day-1 data is superior to the US to begin the modeling. Fourth, I think it is reasonable to state that the Italian data is more honest than the China data. For all these reasons, I’ve chosen the Italian data set as the reference bench mark.
Taking the Italian data set, I’ve extrapolated the data from this to other countries by normalizing the Italian data with a factor of the population ratio. I’m defining the population ratio (PR) as the “Population of a Country” divided by the “Population of Italy”. For China, France, US and India this ratio works out to 23.67, 1.07, 5.43 and 22.56 respectively. This is the resultant graph from this simple model.
Days (Scaled to match exponential infection growth of trend in Italy)
Day-27 in this estimation falls on different calendar dates for each of the countries, due to the normalizing mentioned above. For simplicity, the dates for Day-27 and the number of infections are reported here, which is simply an extract from the above graph.
# Infections (Predicted)
19 Feb 2020
02 Apr 2020
04 Apr 2020
23 Mar 2020
19 Apr 2020
The prediction for China is 1,513,747 infections on 19 Feb 2020 – is this correct!? Actual John Hopkins data for China on 19 Feb 2020 is 74,619 infections. The predicted and actual data for China is off by 95%! Why? I have based the prediction on the Italian data set. For the four reasons mentioned above, it is a good bench mark to start with. This Italian data set predicts the trend for France very well. Based on the actual confirmed cases data, on Day-17, France has an infection level of 14,463 and Italy has an infection level of 17,660 respectively. If the Italian and French data match as per the model, which is based on population ratio and simple scaling, then it probably is a good indictor for other countries. Based on the Italian model, the actual China infection level should have been about 1.51 million! We can look at the data from France and the US and check the efficacy of my model – we just have to wait for 02 Apr 2020 and 04 Apr 2020 for the actual data.
I estimate that the COVID-19 infection in India will reach about 1.44 million by 19 Apr 2020. Whether the actual reported data, from actual testing, matches this or not, is left to the imagination. Math does have the predictive power. Comparison with a model is only as good as the experimental data collected. If the two don’t match, either the model is wrong or the data is wrong!
COVID-19 Infections – Exponential Equations
There is one more mathematical insight that I want to share for predicting the infections. Taking the actual Confirmed Cases data for infections in the exponential growth range for the countries (as above), the exponential best fit can be computed, along with the associated equations.
The exponential equations fit the actual real data remarkably well for France, US and Italy. The R2 variance is in the 98% range, indicating that the fit is good and reliable. I did not bother to plot the real data for China, since the exponential fit is highly tainted, in the sense that the real data tends to follow the Italy-France trend, which is absurd for the population size of China. There are two take aways from this chart. First, the curves follow a nice exponential fit. Two, the exponential equations are all different for each of these countries. The real data from India, if it has sampling integrity, will also have its own unique curve. Sampling integrity means that sufficient testings are done to get the accurate ground level reality for the infections. The first 2 data points for India, in red, are plotted on the graph. We have to get more data points in the next 10 to 15 days (April 02 to April 07) to figure out the equation for India.
I’ll be using a modified Italian exponential equation in a separate article and hope to post the “day to day” correlation between the actual published data and the equation.
COVID-19 Death Analysis
No one likes to think about or even analyze the death statistics. But, in these extraordinary times, we have to undertake this exercise. If we know what a model predicts for the future, which is based on mathematics, we could as intelligent humans take the necessary policy measures to change the trends. We could find medical remedies (more beds and ventilators, medicines, availability of doctors and nurses, transport to medical facilities), we could aggressively work on vaccinations, we could incorporate anti-growth measures such as social distancing and we could incorporate financial remedies to ease the burden of families.
The above graph is from the actual John Hopkins COVID-19 data set. A key trend observed is the asymptote in the China data since the past few days (20 Mar 2020 to 23 Mar 2020). Italy, France, US and India show increasing death toll and we are far from the plateau phase.
Days (Scaled to match exponential infection growth trend in Italy)
The above graph is a one-to-one mapping of the cumulative deaths in the scaled exponential infection growth region. It simply means that we are looking at cumulative deaths when the exponential infections started in each of the countries. France and the US have a very close trend. Maybe in these countries the quality of health care and/or the ability of the people to fight COVID-19 due to inherently present resistance is similar. The US and French data also match up with China on Day-19. But, based on the quantum of population in China, it seems odd, since both the US and France have a fraction of the Chinese population. The China data is most likely wrong or under-reported. Italian death data breaks away dramatically from the US and France data by about Day-12. Either the health care in Italy is not at par with that of the US and France, or that the aged population in Italy has succumbed dramatically to COVID-19. The latter is probably more true, due to numerous reports in the media that age in Italy has been a factor for deaths.
India has just 2 data points in this graph. It is to be seen whether it will follow the Italian curve or the US/French curve.
For the same reasons as that of infections, discussed above, the population normalized data for deaths, taking Italy as the reference data set, yields the following graph.
Days (Scaled to match exponential infection growth of trend in Italy)
As before, Day-27 in this estimation falls on different calendar dates for each of the countries, due to the scaling mentioned above. For simplicity, the dates for Day-27 and the number of infections are reported here, which simply is an extract from the above graph.
# Deaths (Predicted)
19 Feb 2020
02 Apr 2020
04 Apr 2020
23 Mar 2020
19 Apr 2020
Again, as on 19 Feb 2020 the deaths in China is estimated to be 143,899, but the actual data in the John Hopkins data set is 2,116. This is a huge discrepancy. However, as explained in the infection section above, we have to take the actual data with a pinch of salt. The 6,077 deaths in Italy as on 23 Mar 2020 is the actual figure in the data set. For France and US, we can check the actual data with the prediction in the first week of April and confirm the efficacy of the model presented here. The actual data for India from the data set as on 23 Mar 2020 with only 10 deaths is difficult to believe. It does not correlate with the data from the other countries mentioned here. If the Italian model is considered a good bench mark, then we should see about 137,000 deaths in India by 19 April 2020, or by the third week of April 2020.
When will the Deaths stop in India due to COVID-19?
The death data for France, Italy and the US show no asymptote as of 23 Mar 2020. The China data however is showing an asymptote as of 23 Mar 2020. So, if we were to go by the China data, where the exponential growth in infections started around 22 Jan 2020, it’s taken about 60 days for the plateau in deaths. However, the China data is questionable, and the onset of infection might have started in Nov 2019 or Dec 2019. So, the asymptote in deaths can be anywhere from 60, 90 or 120 days from the onset of actual exponential growth. The big question is – whether the exponential growth of infection in China started around 22 Jan 2020 or 22 Dec 2019 or 22 Nov 2019? Based on these timelines, we can make an estimate of the plateau in deaths in these countries, from the onset point of exponential growth.
3 Mar 2020
4 May 2020
3 Jun 2020
3 July 2020
7 Mar 2020
6 May 2020
5 Jun 2020
5 July 2020
26 Feb 2020
26 Apr 2020
26 May 2020
25 Jun 2020
22 Mar 2020
21 May 2020
20 Jun 2020
20 Jul 2020
Estimated Dates for Death Asymptotes
For India, the deaths due to COVID-19 should plateau out by 21 May 2020 or 20 Jun 2020 or 20 Jul 2020. This is based on the assumption that the physical measures of lockdown are similar to what was done in China and probably that in Italy, France and the US. If the quality of lockdown is not on par with these countries, the plateau might happen much down the line.
Factors for lower incidence of Infections and Deaths in India?
As mentioned before, I hope I’m really wrong with the mathematical model and analysis. There are many factors that can increase or decrease the incidence of infections and deaths. It is wishful thinking that the data for India would be magically lower than the raw data trend or the estimations here.
For one, it can be much lower than my estimations, if my simple mathematical model is outright wrong.
If the social distancing and medical care in India is maintained at par with the norms in France, Italy and the US, we can at least expect that the deaths would be on par with these countries, but of course scaled for the Indian population. In this scenario, the deaths should parallel the model presented here.
Another possibility is that a fantastic cocktail of medicines is discovered, possibly from the existing repertoire of medicines, so that the death rate can be dramatically lowered.
A lowering is also possible if a vaccine was discovered for COVID-19 and the entire Indian population is vaccinated in the next 30 days. But, this is a remote possibility.
If the Indian people have a magical immunity to COVID-19, then too we could see a lowering in the death rates. But, as of now, there is no evidence to support this theory.
Closing Thoughts …
The COVID-19 is a surprise to our world. We neither have proven medical treatment nor a vaccine. The only thing we know for sure is that it can spread exponentially and that it causes massive deaths.
There will be nation wide lockdowns, financial strains and stresses in basic necessities of life – food, clothing and shelter. This virus needs both the Government and People to cooperate. We will see either the best in humanity or the worst. It will be a reasonable test for the survivability of the human species. But, the species will definitely make it through, though the losses will be heavy.
It is what it is. The COVID-19 virus is not a living thing. It is just a bunch of molecules, with a protective protein shell and RNA (ribonucleic acid) inside the core (of course there are receptors and other goodies). Without the human cell, it cannot do anything – it cannot duplicate. Once inside, it enters a cell and hijacks the cell machinery, asking the cell to make copies of itself, rather than do the job of the cell. If humans can make semiconductor chips and spacecrafts to fly out into different worlds, they will find a way to stop COVID-19. I’m going to bank on the dedicated scientists to get it done and that too quickly.
I first met this majestic tree in 1982, which stood tall on Bannerghatta Road, just after Basavanapura. It’s been my buddy for 36 years. It was a big old tree back then and more so now. The land adjacent to it is our workplace, from my father’s time. This tree has seen me grow up, it has seen me come and go. It has weathered 100’s of monsoons and has sheltered many a dog, cow, goat, bird, bat and cat. When I arrive at this spot, I know I have come home.
This evening, at about 6:00 p.m., I drove back to my office, but the road was choked with traffic. I finally made it to the gate, only to see my buddy being cut down. I was chocked with emotion. The only thought in my mind was to stop the bleeding.
I met the tree butchers and quizzed them. No one was in charge. One guy, appeared to be the leader and I asked him for the permits to cut the tree. He had none. He told me that his boss, the BBMP contractor, Shekar, had the permits and that I should speak with him. I called Shekar, who stated that he had the permits and that he had given it to the Police and BESCOM. I called the Hulimavu Police station and they told me that they do not know about the tree cut. They asked me to contact the control room (100). I called them and explained the situation. They gave me the number of the Forest Officer In-Charge, Mahesh.
I called Mahesh and explained the matter. I asked him if permits were granted to cut the tree. He was not too sure and asked me send photographs via WhatsApp. He mentioned that some trees were being cut down for road widening. I told him that the tree was being cut in the middle of rush hour (6:00 – 6:30 p.m.) and that it was a serious safety issue. I specifically told him that it was crazy to fell a tree with hundreds of vehicles passing by – buses, lorries, vans, cars, scooters and bikes.
After I had spoken to the Police and the Forest Officer, the tree butchers had quickly gathered the debris on their bikes and vans and scooted away by 6:40 p.m. Why run, if they were following the Law?
I have many troubling questions regarding the maiming of my tree buddy.
Has the BBMP issued a permit to cut this particular tree? If so, who authorized it?
Has the BBMP carried out a honest environmental impact study on the trees to be felled for road widening on Bannerghatta Road?
Assuming that the permit was granted, why did they have to butcher this tree during rush hour, endangering the public?
Why was the Police not present to control the traffic and protect citizens from falling debris?
Why did the tree butchers carry away the cut up portions on their personal bikes and vans?
The tree has a right to live. If it has to be chopped, in the name of city development, let the Government do it with responsibility. There should be an engineer in charge to explain it to the public and share the permits, while the butchering was done. It should be mandatory for the Government to post Police to safeguard the public from injury, while the tree was being cut. Common sense would dictate that the tree should not be cut, when a high density of vehicles were plying by.
If my tree buddy has to be butchered, in the name of development, let it be done with due process, with dignity and within the framework of the Law. I still hope that I can do something, so that what is left of it can live. Maybe if the tree lovers of Bangalore and the World voice their opinion, it would live to see another day. Good night my lovely tree. I know that you are crying and I cry with you tonight.
I recently saw the documentary 13th and it was stunning. The revelations were startling. President Abraham Lincoln abolished slavery in the United States of America on January 31, 1865, through the 13th Amendment. It freed about 4 million Black slaves. However, successive US Presidents successfully maneuvered Government Polices and continued to keep a large percentage of Blacks in abject slavery. The US prison population was 327,000 in 1970 and this jumped to 2,220,300 (more than 2 million!) in 2013. Blacks make up 13% of the US population, but account for 40% of the prison population, which is about 900,000, say close to a million. It is shocking, but true.
How is this related to Poverty in India?
There is a connection and it is political. Poverty has been a political cancer since 1947. Every elected Government, since Independence, has made polices that have perpetuated poverty – some intentional and some not.
There are many definitions for poverty and it can be confusing for anyone. I’ll trust the World Bank’s definition of international poverty line, which was revised in 2015 to US $1.9/day (Rs. 122/day) per person, based on the concept of PPP (purchasing power parity).
Take a look at how the Government of India defines poverty. In June 2014 it was defined as a person earning Rs. 32/day in rural areas and Rs. 47/day in urban areas. A Reserve Bank of India (RBI) report in 2012 computes that 270 million people (22% of population) are below the poverty line of Rs. 33/day. This is consistent with the World Bank’s published data.
At a US $1 to Rs. 64 exchange rate, Rs. 33/day is about $0.52/day per person. The accepted 2015 poverty line of $1.9/day adjusted to 2012 figures is about $1.74/day. How do we reconcile a definition of $0.52/day by the Indian Government to $1.74/day by the World Bank, which is a difference of 235%? It’s apparent that the Indian Government is deliberately under-reporting the % of Indian population below the poverty line.
If we assume linearity in income and % population data, at $1.74/day (Rs. 111/day) the % of population is 74%. At low income levels, linearity is a reasonable assumption.
The truth is somewhere in-between. The % of Indian population below the poverty line is between 22% (Rs. 33/day) and 74% (Rs. 111/day). I’ll mid-point it out at about 48%, for 2012. This translates to about 600 million people in India below the poverty line!
If politicians say that the % of population below the poverty line is less that 22% in 2018, then we know it is not true! It just can’t come down from 48% to 22% in 6 years, which would be a reduction of 54%! There is no way they can justify it, since the Ministry of Statistics and Program Implementation (MOSPI) of the Indian Government does not have any data till date to support a counter claim.
Why is the Indian Government pegging the poverty line to Rs. 33/day per person? It’s simple – because 22% poverty level sounds politically great. If it were taken at Rs.122/day (US $1.9/day), as per the international norm, the % levels would be much higher and this does not sound great to any political party.
I want to further substantiate that the present Indian Government’s definition for poverty of Rs. 33/day is absurd. I spoke to a few of the people I work with, who have come from villages to the city to seek employment. Well, they are from South India and they love rice and sambar, a type of lentil based spicy soup, in their daily diet. They tell me that in the villages, the consumption per person would be about 400g/day of rice and about 200 grams/day of lentil in the form of sambar. Rice is about Rs.50/Kg and lentils (dal) about Rs. 90/Kg. Add to this about 250 grams/day of vegetables at Rs. 25/Kg. This works out to Rs. 44.25/day just on food. What about other things. Let’s take just rent and electricity. In villages, rent may be about Rs.900/month (Rs. 30/day) and electricity Rs.15/day. The basics works out to be about Rs. 89.25/day. One also needs clothes and health care. So, the World Bank estimate of Rs. 122/day seems more realistic than Rs. 33/day of the Indian Government. I don’t have any doubts about it, do you?
The folks I spoke to would be proud to pay for their daily sustenance without doles from the Government. They just want jobs that pay well. They don’t want a hand out of subsidized food supply (Government Ration Schemes or Coupons). Their pride to earn and live well is more valuable to them.
But, poverty is real. The Government is coming up with all sorts of schemes to dole out goodies to the poor and keep them poor. For example, in Tamil Nadu there is the Amma Scheme and in Karnataka there are Indira Canteens, and so on in other states. Such schemes just keep their hunger at bay, but provides no tools for them to progress out of poverty.
The poverty data has always been inconsistently reported and explained since 1947. In the 1950’s about 65% (215 million) of the population was below the poverty line, defined as Rs. 0.6/day per person. In the 1960’s it was 70% (289 million) below Rs. 0.6/day per person. In the 1970-1980’s the figure is reported at 50% and the poverty line was defined at Rs. 1.63/day per person. In the 1990’s poverty was reported at 77%, based on Rs.20/day per person. In the 2000’s, the estimate in 2012 pegs the poverty at 22% based on Rs.33/day per person. Look at the pattern from 1947 – 65%, 70%, 50%, 77% and then 22%. Somebody did some magic in 2012 – political mathematical chicanery!?
I think I have made the case for a poverty estimate of about 48% to 50% at the present time (2018), affecting 600 million people. Of course, I am not an economist or a political analyst or a statistician. So, if anyone disagrees and provides data, I’ll be happy to correct any errors in my analysis.
To pull people of India out of poverty, I think that the Government should re-invest its free doles into more permanent things. In layman’s terms, one way that I see is to create more jobs. For creating more jobs, the new generation must have better skills through education. For jobs that pay better, Companies should be incentivized to do so. If self employed, let the Government re-route the existing free doles to enable people to invest them in working assets, so that it can generate revenue for them.
For salaried and self employed people to earn more, the present 2018 Government of India, should be humble and make practical policies. Their demonetization and GST initiatives have a basic premise – businesses and people are corrupt.
The demonetization policy was a failure. RBI has stated that 99% (Rs. 15.28 trillion or US $239 billion) of the pre-demonetization money (Rs. 15.44 trillion or US $241 billion) in circulation came back to the banks!
I’m a supporter of GST, but the implementation is pathetic. The IT technology behind it is ancient and makes life hell for filers. It’s a system that should grant credit for all purchases, but it does not. Further, even though the businesses have legal invoices and receipts for purchases, they cannot claim credit for all of it, since the GST body wants the seller to upload the sale to the GST site. Why – since the Government thinks we will cheat!
Finally, the officers in the Central Government are still corrupt. Businesses still pay a bribe to get things done in the departments. This nasty practice must stop. So, with honest and practical reforms in GST and the way the Government works, businesses can no doubt create more jobs and also better paying ones. Self employed citizens will thrive. It’s the only way out of poverty, other than being socialistic. India is democratic and it has too large a population for socialism to work. The private sector can do what the Government just cannot.
I think that a little honesty from the Government is needed. It must think real hard and solve the poverty problem. It should stop making policies that keep the poor in poverty. The equation of poverty to votes must end now and forever.