Prediction
for Total Confirmed Cases in India using Linear Variation
Dr
Himanshu Shekhar
Introduction:
Many posts in this blog predicted variation of daily and total confirmed cases
as exponential rise with time. Even after fitting with minimization of
Chi-square for the available data, when extrapolation is made, the curve for
the actual confirmed cases are found to be bending downwards. The actual confirmed
cases are found to be on lower side, as compared to extrapolated simulation. This
clearly indicates that the numerical values are simulated by exponential
variation for the available data, but the slope is always overestimated,
resulting in more deviation as extrapolation goes further ahead in future. Although
a turnaround by 25 July 2020 with very high 21000 daily confirmed cases was
also calculated by Chi-sqaure optimization of normal distribution curve, but
the recent rise in daily confirmed cases are very high, which can send any such
prediction for a toss.
Mathematical Treatment:
Following equation is used for the confirmed cases: C = Aemt, where
A is pre-exponential term and m is activation term. The activation term has
very significant role is ascertaining the slope of the curve. Higher value of ‘m’
results in very high rate of rise of values. Most of the time the value of m is
less than 1 and a typical value is 0.05. In fact, when slope of any such exponential
curve is calculated, dC/dt = Amemt = mC. Clearly, the absolute value
of confirmed cases are simulated but slope is overestimated. The requirement of
correct modelling demands value of variable to be rising with same pace as
exponential curve, but the slope should rise at a slower pace. Such dilemma and
contradiction led to overestimation of confirmed cases, every time after a gap
of 10-15 days. As confirmed cases are definitely rising at a faster pace than linear
variation, because the curve has a rising slope, but the estimate with linear
variation is proposed.
Linear variation: For
fitting linear variation over the available data, the number of confirmed cases
on 15.05.2020 is taken as 0 and the rise at the rate of 10850 confirmed cases. Although
current confirmed cases are rising at a rate of 15000 per day, but lower rise
rate is assumed to compensate for lower rise rate in May and early June.
Additionally, a reduction in daily confirmed cases in India is also
contemplated. The variation is plotted with actual and exponential variation
predicted on 03.06.2020.
The prediction made with
linear variation fits well to the data of June till 22.06.2020 and from this further
prediction is made for total number of confirmed cases in India. The same is
depicted below.
Conclusion: The
earlier assumption of exponential variation is replaced with linear variation
with 15.05.2020 as reference. The daily rate of rise is fixed at 10850 and the
simulated curve till 23.06.2020 is generated. Prediction using linear variation
is shown till 10 July 2020 and by June end 5.0 Lakhs confirmed cases are calculated. It is
also calculated to exceed 6.0 Lakhs confirmed cases by 10.07.2020.
Dr Himanshu Shekhar
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