Doubling rate of COVID-19 cases: how does India fare?
Klaymatrix is pleased to share the guest post titled “Doubling rate of COVID-19 cases: how does India fare?” by Mr Kamal Kumar Murari.
Guest post by: Dr. Kamal Kumar Murari
- Centre for Climate Change and Sustainability, School of Habitat Studies, Tata Institute of Social Sciences, Mumbai, India.
- Labour Market Research Facility, School of Management and Labour Studies, Tata Institute of Social Sciences, Mumbai,India
17 May 2020
Disclaimers: This article presents an independent work, not funded by any individual of agency, and not associated to any institution (public or private). At the moment, when COVID-19 crisis is posing a great danger to humanity, the work in the article attempts to provide a lead in terms of our understanding of how the crisis will unfold in the future. The content presented in the article is strictly for the education and research purpose and do not claim for the accuracy of the predictions. Readers must take the observation and interpretation with caution.The article uses public domain datasets, which is acknowledged in their respective places. I do not provide any guarantee for the accuracy of these datasets.
1. The pattern of COVID-19 cases in India
The current COVID-19 crisis is unprecedented in nature that has impacted almost all countries in the world.The crisis is not only a concern for the public health, but has implications in all form of economic activities and thereby lives and livelihoods. The manner in which the crisis is unfolding, it is hard get any clue regarding what would be total number infected? when will it end in the future? Serious questions that needs to be be answered are the size of health infrastructure needed to deal with serious and critical cases, policy response to deal with mitigation and suppression of the crisis. Policymakers, academicians, researchers are using various modeling platform to understand the nature of the crisis and answers the question posed above.
There are a number of published work exploring the COVID-19 data. Most of these published work have come from experience of China in terms of dealing with the crisis. As the crisis grappling up larger geographical area of the world, more data-driven modeling is also coming up both in published and un-published domain. Visit the site (https://didi.edu.sg) for a detailed description of various data-driven modeling approaches and their applicability of recent COVID-19 data.
The number of confirmed cases of COVID-19, for most countries, is following a exponential growth curve, which is often modeled with the linear regression framework with confirmed cases as a response variable (in logarithmic scale) and time is an independent variable. The slope of the regression line gives the growth rate. Doubling time is another widely used indicator that describes the pattern of COVID-19 pandemic looks like. It is defined as the length of time required to double the number of confirmed cases, assuming nothing changes. This article explores the estimation of doubling time on COVID-19 data for various countries.
Section 2 of the article describes the mathematical background of estimating doubling time. Section 3 shows how the doubling time for COVID-19 progression in India is changing with time. The section also compares doubling time of COVID-19 cases in India with the selected countries of the world. In the article we use country wise confirmed cases from data repository maintained by the Johns Hopkins University Center for Systems Science and Engineering (JHU CSSE). The updated dataset can be accessed from (https://github.com/CSSEGISandData/COVID-19).
2. Mathematical Background of estimating doubling time
The confirmed cases of COVID-19 data in India has a exponential relationship with time. The exponential relationship can be expressed as:
P(t)=ae^r(t)t.....eq.(1)
where a refers to confirm cases at start of the crisis, P(t)is the number of cumulative cases for the day t. The term r(t)refers to the growth rate, which is also a function of time t. The equation can be linearized by taking log on both sides. The linear form of the equation is expressed as:
log(P(t))=log(a)+r(t)t.....eq.(2)
Parameters of eq.(2) can be obtained by regressing log(P(t))l and t. The doubling time for any period can be obtained by applying expression log(2)/r(t). Figure1 shows the fitness of above mathematical expression to the COVID-19 data (confirmed cases) in India.
Figure1: COVID-19 Data in India and its goodness of fit with the exponential model
The positive COVID-19 confirmed cases in India has a high degree of goodness of fit with the exponential function as described on eq.(1), with the variable growth rate. During the first lockdown period, which is from 23 March to April 14, the average growth rate was about 16 %. Doubling time during the fist lockdown period was just over 4 days. During the second lockdown period, which is from April 15 to May 03, the growth rate was roughly half of the growth rate of the first lockdown period and the doubling time as just over 9 days. In the third lockdown period, although the number of cases has increased enormously, but the growth rate was less than one third of average growth rate of first lockdown period. Till May 17 doubling time is 12.47 days.
COVID-19 numbers in India are increasing at an alarming rate. The exponential growth and the rising numbers of the confirmed cases are indeed a concern. A data exploration of COVID-19 cases in India for three lockdown periods indicate that the growth rate has a decreasing tendency. This points out that in the near future India will get its peak of newly diagnosed confirmed cases. This is a kind of argument that many media agencies are pointing out. However, a doubling time just over 12 at a current number of cases 90,648 is also a concern, indicating that by the end of this month total cases in India will be close to 1,80,000, which is a huge number.
The gradual reduction of growth rate can be interpreted as a success of the implementation of lockdown. But,any interpretation of reduction of COVID-19 cases in India is always subject to effective implementation of lockdown or social distancing norm in the future. It is difficult to extend the lockdown in the future as it is severely hurting the economy and thereby impact the vulnerable, however, relaxing lockdown may have a far greater consequences in terms of cumulative number of COVID-19 cases. Therefore, any decision related to extending or relaxing the lockdown has to be taken with greater scrutiny of available facts.
Here I am comparing the daily COVID-19 confirmed in India with three countries: China, Italy, and Spain. These three countries are understood to suppress the COVID-19 crisis. The COVID-19 crisis has started from China, but has taken a serious shape in Italy and Spain. Figure 2, shows the daily confirmed COVID-19 cases for India and the selected countries.
Figure 2: Distribution of daily confirmed cases
From the Figure 1, it is clear that COVID-19 cases in China, Italy, and Spain are in the suppression phase. This means the cases are decreasing day-by-day. Whereas, In India the cases are still increasing. At the moment, the daily number of new cases are adding with over 4000 mark. The other interesting observation that can be drawn from the Figure 2 is the peak of the daily cases. The peak of daily cases in China was around Feb. 23, whereas the peak for Italy and Spain was around the last week of the April month. The COVID-19 cases in India are still in the growing phase with no clear understanding about when it would peak in the future. In fact, the recent 5 days were very alarming as around 4000 cases were adding everyday.
3. Doubling time in India and selected countries
In the Figure 3, I am comparing the doubling time for confirmed COVID-19 cases in India with selected countries. Although India’s doubling time has increased in the past, but still it is below the selected countries that has reversed the pandemic spread. At the moment, India’s doubling time is around 13 days, whereas China, Italy, and Spain has more than 60 days of doubling time.
Figure 3: A comparison of COVID-19 cases in India with selected countries. (Note-The shaded green area represents the COVID-19 growth period in Chine and the orange shaded area represents the COVID-19 growth period for Italy and Spain)
Many government briefings and media reporting take an argument that doubling time in India, with respect to COVID-19 cases, has increased. This article also confirms the calim. However, the results presented in this article do not point to any positive signature with respect to daily increase in COVID-19 cases. The point that I would like to emphasize is that, at the moment, the cumulative COVID-19 cases in India are around 90,000 and if the doubling time is 13 days- this means by the end of the month the cumulative COVID-19 confirmed cases will cross 1,80,000 mark. This does not seems to be a positive note, more particularly in the context of the possibility of release or relaxation of lockdown in the coming future. What is more important is the rate of change of doubling time, as it clearly be seen in the context of China, Italy, and Spain (Figure 3), which is higher than the doubling time in India. The rate of doubling time in India is very slow, which points out that COVID-19 spread in India is a longer issues and in the near future there is no sign of the suppression of the crisis. I hope, in the future, the doubling rate will increase,at least to the mark of 30 days or above, which will indicate the possibility of reduction of COVID-19 spread in the country. Let us keep our fingers crossed.
NOTE: This article is in continuation of series of my work on exploring COVID-19 data, visit https://rpubs.com/kamalkm/607524 for details.
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