COVID
Control in India: Doubling Period Hypothesis
Dr
Himanshu Shekhar
Introduction: The
previous post on analysis of active cases in India gave insight into the
current and desired value of doubling period of each parameter. It became
obvious that subtraction of recovered cases and deceased cases from total
confirmed cases gives active cases. The doubling period for Deceased should be
very high (~ 20-25). The doubling period of confirmed cases must be moderate
and preferably as high as possible. A reasonable value of 12-13 is prevailing
at present, as discussed in previous posts. The doubling period of recovered
cases should be as low as possible, but some finite feasible practical value
may be assigned. It may be in the range of 5-8 in general. Considering various
doubling period, analysis for hypothetical cases, using self-developed
mathematical model, is conducted, using data from Aarogya Setu on 28.05.2020,
as baseline.
Test Run: As
per Aarogya Setu app, on 28.05.2020, total number of confirmed cases in India is
158323, total number of recovered cases are 67692 and total number of death
till date is 4531. For a preliminary study, Doubling Period for Confirmed cases,
recovery cases and death cases are taken as 13, 8 and 12, respectively. This is
reference test case for mathematical model. Then variation of various parameters
are shown in histogram, below.
The height of each column
represents total number of confirmed cases, which is rising. Accordingly, the
recovery figures are also rising. The death cases are also rising with time,
but it is not visible predominantly due to small value, as compared to other
parameters. The most surprising thing is reduction in active cases, which is
visible from height of the green column, with progress of time. The current
active cases on 28.05.2020, stands at 86100, which becomes 62595 on 17.06.2020,
with this hypothesis.
For better appreciation of
the conclusion, the histogram column for each day is separated and presented
below. All four parameters are presented and the reduction in active cases over
period of time is clearly visible.
The same can be appreciated
with the simple x-y plot.
Analysis:
When analysis is conducted by varying the parameters, it must be understood,
that analysis has certain limitations. Here the doubling period of each type of
case is independent of each other in calculation. They are combined to get the
active cases at any date. One peculiarity of this independent of data is that
if doubling period of death cases has increased, ideally, it is good sign. It indirectly
indicates that number of deaths are not increasing at faster pace. But in this
mathematical model, this results in increase in number of active cases on
17.05.2020. For example, for doubling period of death cases as 20, the number
of active cases on 17.06.2020 becomes 67918, which is higher than what is
calculated for doubling period of death as 12.
The most ideal situation is
reduction in doubling period of recovery, which is practically attempted and
which is supported in this mathematical model also. If the recovery period is
reduced from 8 to 7.5, keeping all other doubling period as in previous section
(12 for confirmed cases and 12 for deaths cases), the number of active cases on
17.06.2020 will drastically come down to 15701, as shown below.
Another control can be
exercised by increasing doubling period of confirmed case. If other parameters
are kept same, and doubling period of confirmed cases is changed to 15, the
number of active cases on 17.06.2020 reduces to 1640. This is depicted below.
Conclusion: The
doubling period for confirmed cases, recovered cases and death cases are
adjusted to attain and predict turnaround using mathematical model. It is
observed that the prediction for next 15 days can be easily done based on the practical
values and a turnaround can be visible. The results are tabulated below.
|
Doubling Period (day) |
Numbers of cases as on 17.06.2020 |
|||||
|
Confirmed cases |
Recovered Cases |
Deaths Cases |
Confirmed cases |
Recovered Cases |
Death Cases |
Active Cases |
|
13 |
8 |
12 |
459904 |
382924 |
14385 |
62595 |
|
13 |
8 |
20 |
459904 |
382924 |
9062 |
67918 |
|
13 |
7.5 |
12 |
459904 |
429817 |
14385 |
15701 |
|
15 |
8 |
12 |
398949 |
382924 |
14385 |
1640 |
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