Doubling Rate of Confirmed Cases

Doubling Rate of Confirmed Cases

Dr Himanshu Shekhar

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Introduction:

The figure is extracted from an article in the Times of India entitled “Covid-19 rate in Pune increases to 14 days” with reference TNN | Updated: May 25, 2020, 06:30 IST. The article has mentioned that doubling rate has reduced and Pune is taking more time to double the number of confirmed cases. Additionally, more number of confirmed cases is attributed to more number of testing. It is irony of fact that rather than worrying about increasing number of cases at faster pace and applying more stringent measures to control the Pandemic, complacency and solace is sought through mention of different approach of presenting data. This post emerged out of this article and doubling rate of India and Maharastra is calculated and compiled.

Doubling Period: The doubling rate is defined as rate at which number of confirmed cases becomes twice the earlier value. The days in which number of cases are doubled is a regular measure of the same and the name is a misnomer. It should be mentioned as doubling period. For a given population is doubling period of 5 days is fixed, then every 5^th day the population will be doubled. For a simple analysis, if confirmed case on day 0 is 100, then on 5^th day it will be 200, on 10^th day it will be 400 and so on. A graph is plotted to represent the same for different doubling period. The graph has mention for time needed to reach confirmed case of 100000 from 100 at different doubling period. Higher value of doubling period needs more time for confirmed cases to reach 100000. With doubling period of 5 days, 100 confirmed cases become 100000 in 49.8 days, and it can become 200000 in 5 more days or total 54.8 days. Similarly, at 10 days doubling period, it takes 99.7 days, and to become 200000, it takes 10 more days or total 109.7 days.  

It may be noted that the variations with a constant doubling rate is geometric variation and it is much faster than exponential variation, for larger values of time. This type of curve is very sharp at higher values and is a practically non-realistic estimation. So, the concept of constant doubling rate is a myth, not to be followed in any Pandemic situation. Such predictions will always lead to some solace and statements like doubling period is rising is a good sign, may be a correct but statement with ulterior motives of giving false. The doubling period is checked for India and Maharastra for different time steps.

India:

As indicated, it is possible to calculate the doubling period for India up to 11 May 2020, only, because, the cumulative confirmed cases on 11.05.2020 was 67152. On doubling this number becomes 134304, which is achieved on 25.05.2020. On 12.05.2020, the total number of cumulative confirmed cases were 70756, double of which is 141512, which is not achieved till 25.05.2020. So, the doubling period can be calculated up to 11.05.2020. The value of doubling period, which was around 4 in March 2020, has now reached to around 13 by 11.05.2020. So, the doubling period is improving and it is a positive sign. But let us look at a constant doubling rate right from beginning for India and then plot the actual number of confirmed cases. To match the number of total confirmed cases of 138845, as reported on 25.05.2020, the actual variation of conditions in India is plotted against an overall doubling period.

The slope of actual variation is definitely not matching with the slope of curve with the concept of doubling period. If one numerical value of 25.05.2020 is matched, then before that period, constant doubling rate gives a lower estimated value and after that the estimates goes very high. The doubling period enhancement is just a mathematical exercise to understand the behaviour in positive way, ignoring reality.

Maharastra: Although analysis of India revealed all the nature of various simulation using doubling period approach, but it is applied to the data for Maharastra. The variation of doubling period is presented below. In case of Maharastra, on 13.05.2020, total number of cumulative case was 24427, double of which is 48854. This is achieved on 25.05.2020. However, the double of cumulative confirmed case on 14.05.2020 was (25922x2=) 51844, which is not attained as on 25.05.2020. So, data upto 13.05.2020 is posted for doubling period. The doubling period of the order of 4-6 in March 2020, became 11, at around 10.05.2020.

Conclusion: Doubling period approach is a nice way to manipulate the available data and inculcate a ray of hope by spelling out improvement in situation, but the geometric variation of doubling period approach is definitely not representing the actual situation correctly, in terms of rate of change or numerical values. The exponential variation as used in earlier predictions is a better approach. However, doubling period for both India and Maharastra, both improved from 4-6 in March 2020 to around 12 by 10-12 May 2020.

Dr Himanshu Shekhar