Statistical Analysis of Mumbai between 01.05.2020 and 16.07.2020

Statistical Analysis of Mumbai between 01.05.2020 and 16.07.2020

 

Dr Himanshu Shekhar

 

It was frustrating to see the rapid rise in number of confirmed cases in India at an exorbitant rate. It is not the question of correctness of prediction, but the basic ethics, economy, emotion and essential fibre of India has withered.  I stopped posting, but continued my analysis, without publicly posting it. Today, I got a message from Shri Guru Prakash, one of my friends, in Mumbai, who celebrated his Birthday, this year, under lot of stress, due to the Pandemic. This post is forwarded because of his insistence.

 

Introduction: Mumbai is economical capital of India and it was once upon a time, declared as the Corona Capital of the country, competing with Delhi, for first place. Equally disturbing is the fact that Maharashtra continued to supplement the largest number of confirmed cases in India, but Mumbai displayed a better control, now and Pune, another big city of Maharashtra has emerged as the largest contributor in Maharashtra. Nevertheless, Shri Guru Prakash, provided me with the data from 01.05.2020 to 16.07.2020 and the same is analysed in this post.

 

Confirmed Case Analysis: Confirmed cases in Mumbai is analysed and the trend is plotted below. It is clear that the variation is almost linear, since around 19.05.2020. The case is rising at a steady and probably uniform linear rate.

 

For simulation 30.04.2020 is taken as reference, as the data from 01.05.2020 is made available by my friend. This makes 01.05.2020 as day one for calculation. A power law is fitted and index of fitted curve by Chi-square optimization is obtained as 0.8845. With such closeness to 1 for the index, it is tried to fit a linear curve to the total number of confirmed cases of Mumbai. It is observed that on an average 1260 cases per day is the current rate of diagnosing confirmed cases in Mumbai and it is almost constant from 19.05.2020 till 16.07.2020.

 

 

Daily confirmed cases: The daily confirmed cases is also plotted against time and the variation is almost constant between 1200 and 1400 cases per day from 19.05.2020 till 16.07.2020. The constant value of daily confirmed cases lead to problem with fitment of normal distribution curve for predicting a turnaround.  It leads to a degenerate case and mathematically turnaround, after chhi-square optimization is predicted beyond 2021. I feel that such degenerate mathematics must not be part of the post.

 

 

However, efforts are made to get the total confirmed cases from the optimized normal distribution and a short term prediction is shown below for Mumbai. It predicts attainment of 1 lakh cases in Mumbai by July 2020 and 2.0 lakh cases by mid-September.

 

 

Growth Factor: Growth factor of daily confirmed cases are calculated on daily basis for the data of Mumbai. The values are oscillating widely around 1.0. However, average value for the three months, including July 2020 till 16.07.2020 are all more than 1.0. This indirectly confirms that there is possibility of further rise and potential exists in Mumbai to supplement more and more confirmed cases. However, again this is a mathematical acitivity and is in no way a comment on the scenario in Mumbai.

 

 

Doubling Period: Doubling period is the parameter, which states the time taken for the confirmed cases to get to current level from the value which is half the current value. The doubling period in Mumbai is found to be rising continuously and currently, it is around 39 days.

 

 

However, the doubling period may not a correct estimate of control, so doubling period per lakh is calculated. It says that if confirmed cases become 4.0 lakh from 2.0 lakh in 50 days, then doubling period per lakh is only 25 days. Such rationalization helps in achievement of correct nature of variation.

 

 

It is clear that the doubling period per lakh confirmed cases has stabilized in Mumbai and it is almost constant for quite long period. Minor improvement in numerical value is also observed.

 

Growth Rate: Growth rate based on doubling period is accounted and calculated and it is found to reduce with passage of time. As sometimes, it is criticised that doubling period based growth rate has variation duration in consideration, so, it is better to calculate the growth rate on average of 7-days basis. Both the curves are generated for Mumbai and is reproduced below. The nature of both the curves are same but the 7-days average growth rate curve has lower value numerically.

 

Recovered, Active and Death Cases: The other forms of cases are also analysed. The recovered cases are continuously rising and active cases, after remaining stagnant for some times have declined. In fact, one of my senior colleague Shri JN Verma has given me ring to inform that number of active cases are declining and it is an indication of turnaround. In Mumbai, the active cases are reducing currently and probably, this may be an indication of some sort of control. The death cases are steadily rising and it is an irreversible process.

 

 

Rather than analysing absolute number of cases, the cases in Mumbai are also analysed for percentage values and the plot is shown below. The percentage death is plotted on right axis, which is 10 times enlarged. The value of percentage death out of total confirmed cases is 5.64%. in fact maximum value have touched around 5.86% on 30.05.2020. Percentage recovery is around 70% and percentage active cases is of the order of little less than 25%.

 

 

 

Concluding Remarks: This post and analysis is purely on insistence of my friend Shri Guru Prakash and I still feel that as a true citizen of India, we must demonstrate some social responsibility, to curtail and control further spread of Pandemic. 

In my office, some meeting took place, where, one of the participant got news that the person, whose farewell party, he attended 3 days back has become positive. He rushed to get himself tested and all those, who were there, in the meeting spent that nights under stress. Next day, his report came as negative, but he got news that his driver has become positive. Again he quarantined himself for 7 days to observe any sign. Later, he planned to come by his self-driven car, not chauffeur driven official car. Full office was sanitized and it was a great activity. This narrative is just to sensitize readers to please observe norms and reduce vulnerability of society towards for the Pandemic and Let India win this war, against Pandemic.

 

Thank you Guru Prakash for providing Excel Sheet for Mumbai.

Regards.

 

Dr Himanshu Shekhar