Number
of Confirmed Case per Test for India
Dr Himanshu
Shekhar
Introduction:
In constant effort to analyze the daily and cumulative number of
confirmed cases in India, previous posts in the blogs were made. In
the last post (dated 21 May 2020, entitled “India crossing 1 Lakh
leads to Fresh Prediction”), for reassessing the prediction,
another exponential curve is fitted where pre-exponential factor
was increased 9 times and activation term was halved, as
compared to equation used for the same prediction on 30 April
2020. However, it was pointed out by Shri S. Jayaraman sir, one
of the very senior scientists, that “Instead of plotting total
number against time, plot the number of cases divided by the number
of tests against time”. This post emerged out of that concern
of the reader.
Data Collection:
Although, it is not very convincing that number of testing has any
bearing on COVID-19 spread. With passage of time, more and more
COVDI-19 cases are actually present in India, whether testing is done or not.
Initially, reporting less number may not be due to less number of
testing, but less numbers of infections, itself. More number of
testing can give more number of confirmed cases is a general
conclusion drawn, but as time progresses, number of cases are rising
due to various assorted moves of spread and this fact cannot be ruled
out. So, more than number of testing, it is time elapsed, control
measures, relaxations granted, spread harbingers efforts, etc matter
more. However, the concern for correlating number of testing and
number of confirmed cases has to be looked into, through analysis.
No doubt, I was
following worldometer and the site addresses were also given in my
previous posts. In addition, it is also mentioned that data is now
taken from Aarogya Setu app, also. To get data on number of tests,
News published on
http://indianexpress.com/article/explained/Coronovirus-numbers-explained-india-covid-19-testing-6418807/
web site, written by Amitabh Sinha, updated on 20 May 2020 at 7:11:04
pm, is taken.
Data Analysis:
Daily Number of Tests conducted and daily number of
Confirmed Cases from 09 May 2020 to 21 May 2020, is plotted on
same scale. Both the results are continuously on the rise with time.
The results are quite interesting.
-
On 11 May 2020, there is certain drop reported in number of daily tests conducted, but surprisingly, the number of confirmed cases, reported was more.
-
Contrary to this, between 12 May 2020 and 16 May 2020, the numbers of testing were more but number of confirmed cases have not shown matching rise.
-
On 18 May 2020, a sudden drop in number of test is not reflected in number of confirmed cases.
This type of
behaviour cannot be seen as any correlation. The Pearson coefficient
is obtained for both the data, as 0.3626. So, mathematically, these
two set of data are not correlating.
However, data of 11
May 2020 and 18 May 2020 can be treated as assorted deviation cases.
On both the days, sudden reduction in daily number of tests is noted,
which is due to either incomplete data compilation or due to actual
variation. But giving them benefit of doubt, these two points are
removed from the data and Pearson coefficient of correlation is
obtained for the remaining data. The Pearson Coefficient is obtained
for the remaining data as 0.88423. The correlation has improved and
probably, higher number of test correlates well with higher number of
daily confirmed cases.
Both the curves are shown on different scales and there is no
correlation between them. The rate of rise of number of testing per
day is of the order of 1740, whereas rate of rise of number confirmed
case per day is 213. Definitely number of testing has increased at a
faster pace and it is dependent on technological competence and
initiatives to establish the labs for testing. Contrary to this the
rate of rise of confirmed cases is although derived from testing, but
is dependent on potency of the virus and incompetency of human
efforts to avoid infection. Additionally, the factors, responsible
for spreading it at faster pace are also working simultaneously. A
straight line is fitted to both the data and on 22.05.2020, number of
tests to rise to 106409 and number of confirmed cases may rise to
5704. These numbers are obtained, when these two parameters are
considered independent of each other.
After removal for
those deviations, the ratio of number of tests per unit number of
confirmed cases, on daily basis is plotted against time, with
assumption that, 08 May 2020 is Zero day.
The vertical axis of
the axis represents number of tests needed to get a confirmed case,
on daily basis. A higher value in the initial days indicates that
more number of testing are to be conducted to get a confirmed case,
at that time. As time progressed, the number of tests needed to get a
confirmed case is reduced. This indicates that more number of
infections is there, as time progresses and though correlated with
number of tests, the number of confirmed cases is higher at later
time instant. This clearly indicates that any inference of the type –
“more number of tests resulted in more number of cases” or
“invariant of ratio of number of test to number of confirmed
cases” could not be drawn.
A straight line
curve is also fitted, which has a negative slope. If number of tests
needed to get a confirmed case is represented by TCC and days counted
with zero at 08 May 2020 is D, then following approximate relation
holds.
TCC = 27.77 –
0.7xD.
Although this
relation has Regression correlation coefficient R2 as
0.77155 and Person Coefficient as 0.87838, indicating a poor fit, the
correlation can be treated as rough estimate of current state of
affair.
From this
correlation, 22 May is day number 14 and the value of TCC = 27.77
– 0.7 x 14 = 17.79. If same number of testing is repeated on 22
May 2020, as done on 21 May 2020, then number of confirmed cases on
22 May 2020 will be 5761. If this becomes true, tomorrow, then the
mathematical correlation developed is worth exploration further.
Conclusion:
Daily number of confirmed cases is analyzed in light of daily number
of tests conducted. The values are analyzed from 08 May 2020 to 21
May 2020. It is observed that as time progressed daily number of
tests needed to get a confirmed case is lower. This means that
infection population has increased with passage of time. Had the
number of test needed to get a confirmed case been constant, the
conclusion of dependence of number of confirmed cases on number of
tests could be drawn. In present scenario, a correlation is
developed, from which it is predicted that, if number of tests is
kept constant, then tomorrow i.e. 22.05.2020, there will be 5761
cases. Incidentally in the post, “India Crossing 1 Lakh leads to
Fresh Prediction” indicates daily confirmed case on 22 May 2020 as
5670. We have to wait and watch to see the usefulness of the
mathematical activities.
Dr Himanshu Shekhar
Thanks for your constant concern for the pandemic.
ReplyDeleteFrankly speaking, In great depth, I am unable to understand . But now my mind is waiting for two types of analysis -first what you are doing.
But the second thing is rate of recovery versus confirm cases vs days.
Today we achieved rate of recovery as 40% . It is very satisfying scenario. So I hope if we will reach recovery rate upto 90%, then we will have control over the pandemic.
And I am optimistic regarding the rate of recovery. Like any powerful destructive cyclone, any pandemic has too a limited lifetime. and it will also die its own death. In case of this pandemic, death means very minimum confirm cases per day.
So I will request you to make one separate graph for rate of recovery. Present that graph also. it will work like a silver lining among the dark clouds.
Thank you.
Thanks a lot. You are a constant source of inspiration and encouragement for me. I will definitely work on recovery rate and try to look into active cases than into confirmed cases. Thanks.
DeleteSir,
DeleteReading your analysis regularly, can we have R0 vs t analysis.
Thankyou
Santosh Kumar
Thanks. Recovery is currently a fictitious term. One of my friend, Prakash Kumar stated that earlier three tests were there to mark recovery. Now recovery is announced with only one test. So, the data is inconsistent for Recovery.
DeleteThank you readers and friends. I posted it at 1613. hrs and by 1850, viewership reached 50. Regards.
ReplyDeleteOn 22.05.2020, India registered 6011 confirmed cases, as against 5761, predicted in this post. This situation is not very comfortable.
ReplyDelete