Doubling Time and Its Interpretation for COVID-19 Cases: A Comparative Study in Pimpri Chinchwad Municipal Corporation, Pune, Maharashtra, India

Background: COVID-19, also known as Novel Corona Virus, causes respiratory disorder in humans and has been declared as a global pandemic in the first quarter of the year 2020 by the World Health Organization. As this pandemic persists the second, third and fourth quarters had shown variation in COVID-19 cases. In the first quarter of the year 2021 again there seems to be a rise in cases of COVID-19. So, a comparative analysis from March 2020 – April 2021 of COVID-19 cases has been studied. Methodology: An exponential statistical model was used to calculate the predicted value of COVID-19 using doubling time for a short duration. The cases of COVID-19 were predicted from 10th April 2021 to 10th June 2021 using doubling time and exponential regression method. Results: The distribution of cases showed a curve-linear trend over the last one year. We explored various models like exponential, logarithmic (lo-linear), linear, quadratic, and generalized linear Original Research Article Aphale et al.; JPRI, 33(39A): 75-83, 2021; Article no.JPRI.71471 76 model (GLM) to fit into the observed distribution of cases. Since the distribution of cases was perfectly following a linear trend in each of the four segments, we applied a linear regression model to observed distribution and then predicted the anticipated no. of cases by extending this linear trend to a future period (120 day). With the help of the exponential statistical model, doubling time/rate based on prior 9 days, the predictions of up to 2.61 lakhs cases have been done by the end of June 2021. Conclusion: This study will be useful for the Government of India and Maharashtra state-specific to PimpriChinchwad Municipal Corporation (PCMC), Administrative Units, Frontline health workforce, researchers, and scientists. From this study it has been evident that during the prelockdown period, in the initial stages there seems to be rise in cases. While, during lockdown period it was observed that there was relatively decrease in the number of cases. After the government authorities imposed the unlock strategies the cases began to rise as compared to the lockdown period. Thus, it appears that only essential services should be open for the citizens of India and the state lockdown should be carried on for the next 3 months (April 2021 June 2021).


INTRODUCTION
, also known as Novel Corona Virus, causes respiratory disorder in humans and has been declared as a global pandemic, in the first quarter of the year 2020 by the World Health Organization [1,2]. As this pandemic persists the second, third and fourth quarters had shown variation in COVID-19 cases. In the first quarter of the year 2021 again there seems to be a rise in cases of COVID-19. To help the Government of India and Maharashtra state-specific to Pimpri-Chinchwad Municipal Corporation (PCMC, Fig. No.1), Administrative Units, Frontline health workforce, researchers, and scientists in the management of COVID-19, the analysis of doubling time is required. So, a comparative analysis of the year March 2020 -April 2021 has been studied.
Doubling time of the mentioned duration (March 2020 -April 2021) is studied wherein the number of days required for the number of cases in an pandemic to double, based on the rate of the cumulative increase in the number of cases has been demonstrated. However, the doubling time is a rudimentary analysis of the current proportion of the spread of the virus. Doubling time provides comparable data across time as well as continents at different stages of the spread of infection. On an additional note, the proportion of true cases that are being identified doesn't alter, if the proportion does not change considerably. Doubling time remains constant in uncontrolled exponential growth. Ideally, if measures are being effective, we ought to see the doubling time increasing [3,4]. A higher doubling time means it is taking longer for the cases to double and indicates that the infection is spreading slower. Conversely, a lower doubling time suggests a faster spread of infection. For an infection growing at a constant exponential rate, the doubling time is constant. However, as observed in the COVID-19 situation, due to interventions like social distancing, lockdown, and containment of hotspots of infection, the doubling time fluctuates and is a function of time. It also varies between districts, states, and countries that may be in different stages of infection [5][6][7]. The main purpose of this article is to demonstrate and interpret the doubling time for COVID-19.

Objective
The primary objective of this article was to calculate the doubling time of COVID19 cases and their interpretation.

METHODOLOGY
According to the objective of this study the data was taken from the Website of Pimpri-Chinchwad Municipal Corporation and covers the time from 10th March 2020 to 3rd April 2021 to calculate doubling time/rate based on the prior 9 days [5][6][7].

Short Duration Predicting Analysis using the Exponential Statistical Model
The exponential statistical model used to calculate the predicted value of COVID-19 using doubling time for a short duration. The cases of COVID-19 were predicted from 10 th April 2021 to 10th May 2021 using doubling time and exponential regression method.

RESULTS
The distribution of cases showed a curve-linear trend for the last year (Fig. 2). We explored various model…s like exponential, logarithmic (lo-linear), linear, quadratic, and generalized linear models (GLM) to fit into the observed distribution of cases. Since the distribution of cases was perfectly following a linear trend in each of the four segments ( Fig. 3.), we applied a linear regression model to observed distribution and then predicted the anticipated no. of cases by extending this linear trend to a future period (120 day).

Increasing trend in COVID19 cases in PCMC by days (March 2020 -March 2021)
Details of cases, days, weeks, months 2. March -June2020 2 July-Sept 2020 3 Oct 2020-Jan2021 4 Feb 2021-March2021 Overall March2020 -March 2021 A segment-wise summary of mean no. of cases and % distribution is given below.  On average around 38 cases were added per 9 days in the initial phase (from March to June 2020, Fig. 4.), but it increased to 48 per day in the next 4 months (July to Oct 2020, Fig. 4.) and then furthermore at an average rate of 56 in next 5 months (Nov 2020 to March 2020, Fig. 4.).

Further Interventions and Predicted
Outcomes in COVID-19

CONCLUSION
With the help of the exponential statistical model, the predictions of up to 2.61 lakhs cases have been done by the end of June 2021. Consistency in delivering Health care services in COVID-19 with respect to manpower (physicians), supply of drugs & supplements, occupancy ratio of ICU & Isolation wards or General wards for admission, oxygen supply, the literate ratio of physicians specific to pulmonologist & AYUSH needs to be implemented on a larger scale. Also it is observed that there has been a sudden surge of cases during the unlocking phases. This needs to be addressed on priority basis if further waves of COVID-19 are to be prevented. It appears that only essential services need to be opened for the citizens of India and the state lockdown should be carried on for the next 3 months (April 2021 -June 2021).

CONSENT
It's not applicable.

ETHICAL APPROVAL
It's not applicable.