Analysis and Exploration of Doubling Period for Prediction of Cumulative Confirmed Cases

 

Analysis and Exploration of Doubling Period for Prediction of Cumulative Confirmed Cases

 

Dr Himanshu Shekhar

 

Hope that readers help me in improving my analysis.

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Introduction

Doubling Period is defined as number of days in which cumulative confirmed cases become double. Although mathematically, it may be a fractional number but it is expressed as whole number. This is one of the performance parameter of a country to express the control of Pandemic. Higher doubling period indicates a better control, as rise in case is taking longer time. Currently, although it seems that turnaround has been achieved in India on 07.05.2021 (as predicted in post on 09.05.2021), the doubling period if continuously declining. The control of Pandemic as a function of doubling period is explored in this post.

 

Earlier Turnaround

As India is witnessing second wave of Pandemic, it has already undergone one cycle of turnaround. It has attained a peak in September 2020 and after that continuous decrease in daily confirmed cases is observed. When doubling period data is observed, it was continuously and linearly rising at a constant rate during 15 October 2020 to 25 March 2021. After that the rise has slowed down and in April 2021, it has declined sharply, leading to second wave. Currently the value of doubling period of India is reduced to 46 days, after witnessing a peak (control) value of 187 days on 13.04.2021 (One month back).

 

 

 

When variation of doubling period during 15 October 2020 to 15 March 2021 is assumed to be a straight line rise, the slope of the curve is around 0.87 days of doubling period rise every day. If the slope becomes 1, then cumulative confirmed cases will be under control. In the current situation of second wave, the same slope is to be attained at the earliest occasion to ensure control of Pandemic.

 

 

Simulation and Prediction

Although not very realistic assumption, but it is assumed that now onwards, the doubling period will rise at a rate of 0.87 days per day. Current value of doubling period of 46 days, will become 46.87 days tomorrow, 47.74 days day after tomorrow, and so on. By end December 2021, the doubling period at this rate can reach 250 days. Under this assumption, the value of cumulative confirmed cases are also plotted till 31 December 2021.

 

 

 

It is clear that the current slope of cumulative confirmed cases under the assumption of control, as observed during end of first wave, results in slower rise. Definitely, this slower rise is difficult to achieve in practice. It is also not known that doubling period will be reducing to what level. Overall, an assumption of end of first wave is simulated to predict similar fate of second wave in terms of doubling period. It leads to cumulative confirmed cases of around 3.71 Crores by the end of 2021.

To have better appreciation, prediction for cumulative confirmed cases made from optimized normal distribution curve is superimposed on this doubling period based curve. It is observed that cumulative distribution curve based on both the assumption show almost same value on 31.10.2021. However, variation of both are different. It is clear that calculation based on normal distribution follow the current slope, and the slope reduces to bring the curve to horizontal position end by June 2021. However, the doubling period based approach gives a reduction in slope of cumulative confirmed cases, but the rate of rise is slower, which picks up slowly. The cumulative confirmed cases are shown to be rising continuously. The nature of both the curve are quite different.

 

 

 

Conclusion

It is clear that the end of first wave gave a constantly rising doubling period for India. The value of 0.87 days of doubling period rise per day is assumed for the current second wave also and from 13.05.2021, onwards, this rise in doubling period is assumed. However the cumulative confirmed cases as per this simulation has a kink, a sudden reduction in slope and a continuously rising value. This trend is not acceptable, as such. However, the calculation gives almost similar numerical value, as obtained by prediction based on optimization of normal distribution curve on 31.10.2021. Of course doubling period may not be representing the actual variation, but a control may be possible in this manner only.

 

 

Do read and share. Keep a positive mind in negative body. Take care and be safe. Regards,

 

Dr Himanshu Shekhar