June-July
2020 for Delhi: Modeling and Prediction
Dr
Himanshu Shekhar
Introduction:
The situation in Delhi is analyzed using data till 09.06.2020, in the previous
post. However, the confirmed, recovered and deceased cases of Pandemic is
modelled using exponential variation for Delhi. The parameters of exponential
variation is finalized for each case using minimization algorithm for
Chi-square values from actual data. The derived parameters are used for the
prediction of different types of cases in June and July of 2020. The exercise
is purely mathematical in nature, assuming that prevailing optimized parameters
of exponential variation is valid for the mentioned period.
Mathematical
modeling: The data of confirmed, recovered and
deceased cases for Delhi from 01.03.2020 till 08.06.2020 is collected and
plotted to get their variation. It is observed that except confirmed cases, all
other cases have sudden jumps and stagnations, indicating discontinuous
acquisition of data. However, the available data is plotted. It may be noted
that confirmed cases are a function of number of tests conducted, and this type
of variations are avoided in current analysis. The available data is taken
assuming that the reported values are indicator of true situation.
The
number of active cases are obtained by subtracting recovered and deceased cases
from total confirmed cases. For each of the three basic cases, namely confirmed,
recovered and death, exponential fit of the type: Cases = Aemt,
where t = time in days counted with 01.03.2020 as 1, A, m are constants to be
optimized using Chi-square parameter, is used. For each case, optimization
solver is run for minimization of Chi-square and values of exponential
parameters A and m are obtained for each case, as shown below. The activation term (m) for confirmed cases and recovered cases are similar and death cases have higher activation terms. the pre-exponent term (A) is the highest for confirmed cases, around half of that for the recovered cases and almost negligibly small for death cases. The fitted curve
is depicted in the figure below.
Prediction:
From these modeled exponential parameters for confirmed, recovered and death
cases, active cases are calculated. The variation for various types of cases
are plotted below for June 2020 and July 2020.
The values
are obtained for various milestones in June and July 2020 for Delhi. The
results are tabulated below.
|
Date |
Confirmed |
Recovered |
Death |
Active |
|
15 June 2020 |
44486 |
17560 |
1438 |
25488 |
|
18 June 2020 |
52282 |
20709 |
1833 |
29740 |
|
01 July 2020 |
105261 |
42327 |
5258 |
57677 |
|
13 July 2020 |
200819 |
81882 |
13905 |
105032 |
|
21 July 2020 |
308907 |
127126 |
26592 |
155189 |
|
30 July 2020 |
501451 |
208528 |
55146 |
237778 |
Conclusion:
Using Chi-Square minimization, recovered, death and confirmed cases of Delhi is
modelled as exponential variation. The active cases are calculated for certain
assorted time steps in June and July 2020. Confirmed cases is calculated to
cross 50000 on 18.06.2020, 100000 on 01.07.2020, 200000 on 13.07.2020, 500000
on 30.07.2020. Active cases are calculated to be crossing 100000 on 13.07.2020.
However, these values may be exaggerated numbers in light of other controlling
factors, which may restrict the unabated exponential rise of all types of cases.
Dr
Himanshu Shekhar
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