Critical Analysis of Daily Growth Rate and Doubling Period in India till 30.04.2021

 Critical Analysis of Daily Growth Rate and Doubling Period in India till 30.04.2021

 

Dr Himanshu Shekhar

 

My sincere thanks to all the readers. Do comment if any specific analysis is needed.

 

Introduction

After 20 July 2020, I placed my blog on 30.04.2021 to find that despite absence of lockdown, my acquaintances are ready to read about analysis. The blog view exceeded 100 in 30 minutes and reached above 200 in 8 hours. As per that analysis, the turnaround is predicted by 29 May 2021 with peak reaching slightly above 7 lakhs. As promised, I am extending the analysis further by calculating some more factors to give insight into various other aspects of spread and rise in infection. In this blog, I am concentrating on two factors – one is doubling period and another is daily growth rate. Doubling period is expressed in number of days in which the value has doubled from original values. The growth rate is expressed in percentage at which a daily growth can result in the expressed rise. It can be calculated on weekly basis or from the doubling period data.

 

Doubling period

It may be noted that higher doubling period means control over the situation. If a particular value takes longer time to double, the rate of spread is slower. With this in mind, doubling period is calculated and presented below.

 

It is clear from the graph that doubling period is continuously rising till 07.04.2021, when it reached 188 days. This was showing a good control, during this period, when rise on doubling period was observed. However, then it starts declining, meaning values has tendency for faster growth after this. Some infection booster has grasped the society.

However, this is not the correct picture. This method of calculation says that if duration for values to become 200 from 100 and 200000 from 100000 are 15 days, then doubling period is same. However, the second case represents a more severe condition. To get rid of this discrepancy, an attempt is made to find out doubling period rationalized to 1 lakh infections. And the plot is given below.

 

It is clear from the plot that doubling period per lakh infection has gone down in 2020 and reached a minimum value of 1.174 days on 02.10.2020, after which it was rising continuously. This was the period, when first peak for infection was observed in India. A rise in doubling period is a good sign. However, the doubling period attained a peak on 24.03.2021 as 3.071 and then it started declining. It indicates poor control of infection in India after 24.03.2021.

 

Daily growth rate

Calculation of daily growth rate resembles calculation based on compound interest rate formulate taught in high schools. Daily growth rate is quite fluctuating for total number of confirmed cases. A weekly trend of rise around Thursday and fall on Tuesday was predicted in the blog, in a previous post. So daily growth rate is calculated based on weekly variation, so that daily growth rate from one Monday to next or one Thursday to next … is calculated. A lower growth rate indicates control and is desirable. Daily growth rate based on weekly data is shown below.

 

 

It is clear that this value is continuously declining and it reached a value much lower than 1%. It remained constant at a lower value for 15-20 days in January 2021 and attained a value of 0.103% on 17.02.2021, after which it started rising. It clearly indicates that opening of mall, gym, schools and election played a major role in such growth. The growth has reached to a level of above 2.063% now, by 30.04.2021.

However, the above calculation is criticized for being based on constant time step. But that is also a good measure of rate of rise. Of course time-independent daily growth rate can also be conceived. Another approach for calculation of daily growth rate is based on doubling period. The graph for the same is shown below.

 

  

This graph is continuously declining. It indicates a good control, as rate of rise is continuously declining. However the lowest value is observed on 07.04.2021 as 0.369% and it started rising thereafter. Since it is based on doubling rate, it follows the trend depicted by doubling period. However, it is clear by any analysis that control is somehow lost by the first week of April 2021.

Conclusion

Considering doubling period, it is observed that some infection booster has been active during 24.03.2021 to 07.04.2021, which reduced the doubling period. It is ironical but somehow festival of holi was there on 29.03.2021. Additionally, marriages also started during that period. If daily Growth rate is observed, it is also showing almost similar trend. Daily growth rate based on weekly bases of on the basis of doubling period, both are indicating poor control in April 2021. Any thought of turnaround will be indicated first by these critical factors of the current pandemic in India.