Shekhar's Science Blog

Friday, July 9, 2021

Lock Down Needed

 

Lock Down Needed

 

Dr Himanshu Shekhar

 

Thank you readers for the giving me unconditional support through viewing my analysis. Please note it is a purely mathematical exercise, by converting a discrete and unconnected data using continuous distribution, for prediction as well as assessment.

 

Introduction

Till one week back, I was optimistic about non-existence of third wave in light of reduced number of daily confirmed and deceased cases.

 

https://www.blogger.com/blog/post/edit/3805764448716920548/7039368766954804280

 

However, as indicated in last post, neither the daily confirmed cases reduced below 10000, nor the percentage deceased is reduced to less than 1.0%. In light of this, the situation of last year is likely to be repeated. Lockdown was lifted in June 2020 and peak came somewhere in September 2020. Rather than that one more month of lockdown extension would have given a better result, last year. This year also, the daily confirmed cases has not gone down to expected level (10000) and with opening of lockdown, where the slogan of “full hospital and empty hotels” is replaced with “empty hospitals and full hotels”, the third wave is likely to sweep India. It is purely negligence of people, who are eager to go to tourist spots to support the dying tourism industry at the cost of third wave in the country. Either government should do or people should restrain themselves.

 

Current Situation

Daily confirmed cases are monitored with respected to my prediction made on 09.05.2021 and after two months, the cases would have gone down to less than 10000 cases. However, in last 18 days, the value is around 40000, which is 4-times higher than prediction. More than the numerical value, the trend of stagnation is visible, which may be fatal.  




The stagnation may be responsible for subsequent rise in the values. Same is the situation with daily deceased cases. This is also stagnating around 1000. Although downward trend is observed but the value is still much above 1.0%. The current value is 1.86%, and it is going above 2.0%, also.

 



Wave Calculation

The comparison of first and second wave gave a 4-fold increase in amplitude and time duration is reduced by a factor of 2.7. However, with same factor, the third wave will come faster and it is an unlikely assumption. It is depicted below but is irrelevant.

 



Second assumption of third wave with equal magnitude as second wave is at present valid. If instead of going further down, daily confirmed cases pick up to rise from this point, the likely curve is shown below. However, pick up time will be later than predicted by this assumption.

 


The basic problem with such wave type assumption is that, the duration between any two consecutive waves could not be ascertained correctly, by any formation. If wave starts then further prediction is possible, but the in-between period is not following any variation. The valley between first and second wave is slightly skewed with fall of first wave is much slower than the rise of second wave. In fact, now we are at the falling curve of second wave, which has slowed down. The wait is for the rise to happen. If an optimized symmetrical parabolic curve is fitted to the curve, the lowest point of daily confirmed cases is observed on 20.07.2021 with minimum of 20000 and now we have to wait and watch the rising trend of daily confirmed cases.  

 



Conclusion

The third wave can be controlled only by active participation of people. With current trend of daily confirmed cases, third wave is being invited by the stagnation of daily confirmed cases. The cases are not going down, as expected and now only rise is expected by the type of negligence displayed by various parts of the country. It will be fine if a 15 days lockdown is imposed to bring the daily confirmed cases to less than 10000. All the best. Stay safe in unlocked India.

 

Dr Himanshu Shekhar

 

Saturday, July 3, 2021

No Third Wave Reiterated

 

No Third Wave Reiterated

 

Dr Himanshu Shekhar

 

Thank you readers for the giving me unconditional support through viewing my analysis. Please note it is a purely mathematical exercise, by converting a discrete and unconnected data using continuous distribution, for prediction as well as assessment.

 

Introduction

I am regularly posting on my blog about different forms of mathematical analysis to understand the trends in confirmed cases, deceased and third wave. Analytical approach is presented and prediction tools are developed for the same. I made a prediction on 09.05.2021 about the turnaround using normal distribution curve and the same is still valid. However, rate of fall of daily confirmed cases declined in recent past. The daily number of deceased, which was around 1% till turnaround of second wave of 07.05.2021, increased to around 4.0%. At present also it is above 1.5%. The possibility of third wave is also predicted using damped vibration equation with different logic. This post is to take stock of daily confirmed cases and daily deceased cases. The main emphasis is negating possibilities of third wave through various arguments.

  

No Third Wave

Third wave is hyped by all corners, but I am still not able to understand the origin of this innovative concept, which gripped the nation. We as Indians have to work collectively and think as a community to fight against this pandemic. We are doing it and the third wave is going to be a myth, in light of strict adherence of COVID-Appropriate Behaviour by Indian citizens.

 

https://himanshushekharscience.blogspot.com/2021/05/prediction-of-third-wave-in-india.html

https://himanshushekharscience.blogspot.com/2021/06/india-on-path-of-recovery-from-second.html

 

Two approaches for predicting third wave was presented - (i) Amplitude multiplied by 4 and duration reducing by a factor of 2.7 and (ii) Third wave of equal amplitude and duration as second wave. The situation as on 03.07.2021, as per both the approaches is shown below.

 

 


 

First approach seems to be negating presence of third wave, if by the end of next week, daily confirmed cases drops to less than 10000. Hopefully the slow fall of daily confirmed cases will prevent further rise in number of cases, merging with the predicted third wave.

 

 


 

As per second approach, a little longer wait is needed. But as per declining tendency, any rising trend is again very unlikely, as per the created mathematical trend.

In addition to this mathematical calculation, following arguments are put forth, which negates presence of any third wave in India:

  1. People are following COVID-Appropriate Behaviour meticulously.
  2. Awareness has penetrated to general public to control the pandemic.
  3. The cases are discrete, isolated and discontinuous and any prediction made by anybody (including me) has no basis, except for the trend analysis.
  4. Mathematical trend denies existence of any rhythmic pattern for the third wave.
  5. Making infections less than a critical threshold value may prevent any subsequent rise.
  6. Rise in lethality leads to reduce spread for such pandemic.
  7. Darwin’s Survival of the Fittest prevailed and all with weak immunity have already suffered. The remaining lot has higher resistance.
  8. A large population is already infected and cured from the disease.
  9. A large number of vaccination is already administered.
  10. Claim of rise in September, being a festival season may prove wrong by participation of people, in exactly same way, as it was executed last year.
  11. Media has also diverted attention away from pandemic, as people are passive and neutral to pandemic related news.
  12. Addressing third wave, as dangerous for kids is also based on wrong notion of non-vaccinated mass and less immunity. Kids have higher immunity, as explained in my video, some time back.

 

Despite all correct, pleasant and encouraging vibes, it must be kept in mind that even 1 infected person can spread it to 1000. So with people’s participation, only control can be exercised. But Third wave is highly unlikely to sweep India, in near future, if people are alert.

 

Daily Confirmed Cases

Daily confirmed cases were reviewed several times in past 2 months in various posts.

 

https://himanshushekharscience.blogspot.com/2021/05/covid-under-control-in-india.html

https://himanshushekharscience.blogspot.com/2021/05/salient-parameters-one-week-after.html

https://himanshushekharscience.blogspot.com/2021/05/comparison-of-confirmed-cases-with.html

https://himanshushekharscience.blogspot.com/2021/06/covid-under-control-in-india-with-rider.html

https://himanshushekharscience.blogspot.com/2021/06/india-below-1-lakh.html

 


 

The situation on 03.07.2021 is reviewed again through plots. The rate of decline of daily confirmed cases is slower than prediction. The daily confirmed cases are still above 40000, where it is predicted to be less than 10000, as per optimized normal distribution curve on 09.05.2021. The cumulative confirmed cases is also moving as per prediction. However, we have to keep our fingers crossed to conceive any rise ion daily confirmed cases, due to any unwanted case-booster activities including religious, social or cultural activities.

  


 

Daily Deceased Cases

The daily confirmed cases is now less than 1000. However, as percentage of daily confirmed cases, it is around 1.58%. This number must reduce to less than 1.0%, to indicate a better immunity and strength of the population. Ideally, the value should be around 0.5% and daily deceased must reduce to (40000x0.5/100 =) 200. Actual value is 738, which needs 4-fold decrease, urgently for the current situation.   

 


 

Conclusion

The third wave can be controlled only by active participation of people. With current trend of daily confirmed cases, third wave is unlikely to happen. People have to be vigilant and active with commitment to fight any case-booster activities. The slow decline of daily confirmed cases is a concern, but reduction is always a welcome data. Similarly daily deceased as percentage of daily confirmed cases must reach 0.50% to indicate reduction in fatality. I am not finding any reason to see any third wave in India, if people of India desires so. All the best.

Stay safe in unlocked India.

 

Dr Himanshu Shekhar

Saturday, June 26, 2021

India on Path of Recovery from Second Wave and an Improbable Third Wave

 

India on Path of Recovery from Second Wave and an Improbable Third Wave

 

Dr Himanshu Shekhar

 

Thank you readers for the giving me unconditional support through viewing my analysis. Please note it is a purely mathematical exercise, by converting a discrete and unconnected data using continuous distribution, for prediction as well as assessment.

 

Introduction

It has been my pleasure to carry out the optimization study on daily confirmed cases and fit a normal distribution curve with optimized mean, standard deviation and peak. The prediction was made on 09.05.2021 (https://himanshushekharscience.blogspot.com/2021/05/covid-under-control-in-india.html ), to predict a peak daily confirmed cases of second wave as around 4 Lakh. There are three aspects of concern – daily confirmed cases, which must decline below 1000 for entire India, daily deceased number, which must come down below 50 for the entire India and the possibility of third wave. This post discusses all the three aspects.

 

Third Wave Prediction

I have made an attempt to predict advent of third wave using damped vibration equation with varying amplitude and varying frequency. This was posted on 30.05.2021 and it was one the most viewed post. Thanks to all the readers.

https://himanshushekharscience.blogspot.com/2021/05/prediction-of-third-wave-in-india.html

 

An attempt is made to again carryout calculation for the prediction of a third wave using data up to 25.06.2021. Correction to the amplitude and frequency is applied and prediction is made.  The amplitude is assumed to be increasing by a factor of 4 and the time duration is found to be reducing by a factor of 2.7.

Wave

Amplitude

Duration

End date

1

100000

320

05-03-2021

2

400000

119

01-07-2021

3

1600000

44

14-08-2021

4

6400000

16

30-08-2021

 

Third wave, even if it is coming, is mathematically found to be more severe in terms of daily confirmed cases (Amplitude). However the duration will be very small for this. The amplitude is found to be too high and the duration is also very small with peak being attained on 24 July 2021. This is mathematical prediction, which seems infeasible.

 



 

If a third wave similar in nature to second wave in terms of amplitude and frequency is expected, then the variation has different connotations. Around 4 lakh daily confirmed cases, and cycle time of around 120 days gives a curve matching to the second wave. The same is extrapolated to give a peak on 07.09.2021 and third wave is likely to end by 01.11.2021.

 

 


 

This perception is also likely to be infeasible, as the number of infected and vaccinated people has risen to such a large extent that spread of infection will not be effective, enough to realize a third wave. The only concern remains the slow decline of daily confirmed cases, which must be curtailed and controlled by the participation of people. The second wave should quickly attain a daily confirmed cases of less than 1000 cases. The faster, it is attained the better it will be. The daily confirmed cases and daily deceased are also reviewed.

 

Daily confirmed cases

Daily confirmed cases are monitored at regular interval after 09.05.2021, to confirm deviation from prediction. The review dates of subsequent posts were 14.04.2021, 29.05.2021, 05.06.2021 and 12.06.2021. The link to those posts are given below.

https://himanshushekharscience.blogspot.com/2021/05/salient-parameters-one-week-after.html

https://himanshushekharscience.blogspot.com/2021/05/comparison-of-confirmed-cases-with.html

https://himanshushekharscience.blogspot.com/2021/06/covid-under-control-in-india-with-rider.html

https://himanshushekharscience.blogspot.com/2021/06/india-below-1-lakh.html

 

 

 


 

The daily confirmed cases were following the predicted curve till, last week and the fall of curve was represented correctly by the optimized normal distribution curve. However, in recent past the daily confirmed cases showed a slower pace than expected and the reduction in decline rate is a concern. The daily confirmed cases are 51667 on 25.06.2021. However, daily and cumulative confirmed cases have followed the prediction for the last two months, correctly. The daily confirmed cases is exceeding prediction now.

 

 


 

Number of Deceased

The number of deceased was found to be following the daily confirmed cases. It was clear that around 1% of daily confirmed cases was exhibited as daily deceased. However, this ratio was disturbed after peak of second wave on 07 May 2021. The number of daily deceased had not declined at same rate as daily confirmed cases were declining, resulting in rise in percentage deceased.

 

 


 

 

For finding a relation, between trends of percentage deceased, an equation is developed on 29.05.2021 and it was followed for next 10 days, only.  The situation is reviewed on 05.06.2021 and the trend was valid.

https://himanshushekharscience.blogspot.com/2021/05/comparison-of-confirmed-cases-with.html

https://himanshushekharscience.blogspot.com/2021/06/covid-under-control-in-india-with-rider.html

 

However the trend of percentage deceased as percentage of daily confirmed cases, was valid for only 10 days. Then there was a sudden peak in percentage, followed by a period of large percentage. The deviation on 12.06.2021 was observed and mentioned in the following post.

https://himanshushekharscience.blogspot.com/2021/06/india-below-1-lakh.html

 

The current value is lower than the predicted values, but still the percentage deceased is currently 2.57%. This ratio must come down below 1.00%.

 

 


 

 

Conclusion

The third wave can be controlled only by active participation of people. The trend of previous two waves with increasing amplitude and reducing time-duration gives an infeasible solution mathematically for the third wave. A third wave similar to second wave is likely to sweep India, but it can become improbable with masks are used and social distancing norms are followed. The daily confirmed cases is not falling at a faster pace. This may be one concern, but decline is more or less steady. The daily deceased is reducing but it should reach below 1.0% of daily confirmed cases. Overall, I feel third wave is unlikely and control exercised by India is very good in June 2021.

Stay safe in unlocked India.

 

Dr Himanshu Shekhar

Saturday, June 12, 2021

India below 1 Lakh

India below 1 Lakh

 

Dr Himanshu Shekhar

 

Thank you readers for the giving me unconditional support through viewing my analysis. Please not it is a purely mathematical exercise, by converting a discrete and unconnected data using continuous distribution, for prediction as well as assessment.

 

Introduction

It has been my pleasure to carry out the optimization study on daily confirmed cases and fit a normal distribution curve with optimized mean, standard deviation and peak. The prediction was made on 09.05.2021 (https://himanshushekharscience.blogspot.com/2021/05/covid-under-control-in-india.html ), to predict a peak daily confirmed cases of second wave as around 4 Lakh. Although I was expecting a decline to a level of 60000 by the end of the current week, but the reduction was not that fast. Additionally, the number of deceased has shown an abnormal trend in last two days, shooting up at a very fast pace. These two aspects will be discussed in this post.

 

Daily confirmed cases

Daily confirmed cases are monitored at regular interval after 09.05.2021, to confirm deviation from prediction. The review dates of subsequent posts were 14.05.2021, 29.05.2021 and 05.06.2021. The link to those posts are given below.

https://himanshushekharscience.blogspot.com/2021/05/salient-parameters-one-week-after.html

https://himanshushekharscience.blogspot.com/2021/05/comparison-of-confirmed-cases-with.html

https://himanshushekharscience.blogspot.com/2021/06/covid-under-control-in-india-with-rider.html

The same is repeated on 12.06.2021, again. The daily confirmed cases followed the falling limb of normal distribution, correctly. Although falling trend continued in last week till Tuesday (08.06.2021), after which it stagnated at around 92000 daily confirmed cases. One of the most satisfying thing is that despite unlocking various facilities, markets and offices, the weekly rise on Thursday is controlled. This shows that India has control over the weekly rise in daily confirmed cases. However, the cases failed to drop and stagnated. If it would have followed the falling trend, the case would have been less than 60000 by now (12.06.2021).

 

 


The cumulative confirmed cases, were also monitored regularly, which was showing a gap from the prediction. The most appealing part of the cumulative confirmed cases is that, the actual values are less than prediction and India is witnessing a faster control than expected by prediction. The same trend must continue.

 


 

 

Number of Deceased

The data on number of deceased has been a major concern for India. Despite fall in daily confirmed cases, the daily number of deceased is not falling at same rate. Earlier it was following the same trend as that for the daily confirmed cases, but after attainment of peak, the fall in daily number of deceased stopped. The number of deceased was maintaining a value of 1% of the daily confirmed cases, but it is rising now. The reporting of 6148 deaths two days back has been a major concern and it may be an accumulated figure of earlier 2-3 days, which were inadvertently left in accounting. However, after this also the cases clocked a value of 3403, which is higher than earlier values of around 2200 daily, for period prior to  10.06.2021. It is sure that fatality of second wave is much higher and the same is still maintained.

 

 


 

The number of deceased as percentage of daily confirmed cases was showing a quadratic rise and it was also modelled as a quadratic equation. However, for the last two days the values were much higher than prediction by the derived formula. The uncertainty prevails and the control on daily number of deceased is not available. On the date of adjustment the percentage touched 6.54%, while yesterday it was 3.71%. Both the values are much higher than prediction.

 

 


 

Conclusion

Daily number of confirmed cases are declining as per normal distribution curve. The traditional weekly rise in values on Thursdays is skipped in last week. However, rate of decline in cases have slowed down. Hope that unlocking is not holding daily confirmed cases, up. The fatalities are on the rise and compared to earlier situation, when there were scarcity of drugs, beds, and oxygen, now situation is much better. Despite this rise of number of deceased is a matter of concern. People are fed up now and so is CORONA, as attention of general masses is shifting to other dimensions. Daily deceased must decline to less than 500 at the fastest possible pace, to offset the fear. I hope that by the end of next week say by 20.06.2021, number of deceased will drop to 400 cases daily and daily confirmed cases will come below 40000. I pray that unlocking under people’s surveillance and COVID appropriate behavior may get us out of the current wave, fast.

Stay safe in unlocked India.

 

Dr Himanshu Shekhar 

Saturday, June 5, 2021

COVID under Control in India with Rider of Number of Deceased

 

COVID under Control in India with Rider of Number of Deceased

 

Dr Himanshu Shekhar

 

I am thankful to my readers and viewers for their valuable opinions and more than 350 views on previous post entitled  “No Third Wave in India”.

 

Introduction

The prediction made on 09.05.2021, almost one month back about the possibility of a turnaround in daily confirmed cases on 07.05.2021 was well received by my readers (https://himanshushekharscience.blogspot.com/2021/05/covid-under-control-in-india.html ). The predictions were based on optimization of a normal distribution across data of daily confirmed cases.  The current post is generated to take stock of the deviation from predicted results. Additionally, the number of deceased is a major concern and the numbers are not reducing in proportion to reduction in daily daily confirmed cases.

 

Confirmed Cases

 A recap of prediction of prediction was made after one week (https://himanshushekharscience.blogspot.com/2021/05/salient-parameters-one-week-after.html ). The prediction made on 09.05.2021 is plotted against daily number of confirmed cases, till 05.06.2021. The declining limb of the falling normal distribution is shown by the actual daily confirmed cases. It is really satisfying to find that the prediction is valid for over a month. The superimposed curve is shown below.

 


 

Parallel to this, if cumulative daily confirmed cases are calculated from the optimized normal distribution curve. This cumulative value is also plotted against actual cumulative confirmed cases. The actual cases are found lower than prediction and the difference between actual and prediction is continuously rising. This indicates that the actual cases are much lower and this trend must continue till June end of 2021 for better control of pandemic in India. This is really encouraging to see that the turnaround and declining number of cases are well within control.

 

 


 

Analysis of Deceased

If daily number of deceased are plotted along with daily confirmed cases, close matching of both was observed till the turnaround. When confirmed cases were rising number of deceased were also rising and vice-versa. However, after turnaround, daily confirmed cases declined but corresponding decline in number of deceased were not observed. It was pointed out in a previous post by end of May 2021 (https://himanshushekharscience.blogspot.com/2021/05/comparison-of-confirmed-cases-with.html). The same is extended for 06.06.2021.

 


 

The daily number of deceased stagnated at around 3000 cases and it is not declining at faster pace. This leads to gradual rise in percentage positivity rate of the country. As positivity rate is continuously rising, the same is modelled as a quadratic equation in the referred post. The same equation is valid and currently the positivity rate is around 2.55%.  

 


 

Conclusion

The daily confirmed cases are following the declining trend and we have to keep the finger crossed to see proper matching of actual cases with the prediction. So long as no surprises are visible, due to opening up of lockdown, India can be said to have controlled the Pandemic. However, the number of daily deceased cases is a matter of concern. The continuous rise in positivity rate of deceases cases as percentage of daily confirmed cases is really following a disturbing trend. The daily number of deceased has to drop. The actual situation is mortality of infected persons within one month of their long hospitalizations. This trend must be reversed or stopped. The current status of slowly unlocking the country must not result in any rise in daily confirmed cases. With this hope I reiterate that there will not be any third wave in India, if COVID appropriate behaviour is followed. My readers have expressed concern about a possible third wave in Sept-Oct 2021 due to (i) festival season (ii) postponement of many marriages to that period (iii) reduction in in-built immunity due to recovery from Pandemic, after 6 months. Let’s us hope for the best.

 

Stay safe, stay healthy, follow social distancing, and remain connected through social media. All the best.

Regards,

Dr Himanshu Shekhar

Sunday, May 30, 2021

Prediction of Third Wave in India

Prediction of Third Wave in India

 

Dr Himanshu Shekhar

 

I dedicate this blog to my Math Professor Late Shri SB Singh of MIT, Muzaffarpur, Bihar who nurtured and honed my mathematical skills.

A predictive approach using sinusoidal variation is attempted in this post of the blog. This post was created due to absolute faith of my Friend TK Sadhana Singh in me and my calculations. The encouragement from each reader is my asset and I look forward for more input to give me correct direction for prediction.

 

Introduction

England has claimed to have achieved very nice progress in vaccination, which resulted in poor penetration of virus at the general health of people. Although England has attributed control, due to lockdown, but at the same time, now vaccination is stated to be the main reason for non-fatal next variant or wave in England. India is not able to progress rapid vaccination due to vast population and scarcity of vaccines. However, based on the available data till date, an attempt is made to predict possibility of third wave, using various mathematical technics. As number of data-points specifying waves is insufficient, some assumptions are made for the prediction. First an attempt is made to model both the waves in India, using single equation of damped vibration.

 

Nature of Waves

India has seen two waves, each attained a peak, followed by a decline. The reasons for advent of second peak was neither known nor investigated, properly. In absence of any correct social engineering parameters known, it is purely mathematical exercise, which is repeated. At first nature of the variation of daily confirmed cases are observed. Although normal distribution curve fits well, but this is not sufficient to predict the re-occurrences and wave nature. Normal distribution has only one peak at mean position with proper standard deviation representing span of each wave. To get rid of this, damped vibration equations are fitted, after assessing the nature of both the waves. First concern is peak confirmed cases in both the waves, which has a multiplication factor of 4. First wave has peak cases of 1 lakh, while second wave has 4 lakh peak daily cases. Second feature is span of the wave on time scale. Time span of both the waves has a factor of 4.

For modelling this, curves are generated incorporating these features, where peak value of each wave changes and so is the time-scale. First curve represents equation of the type y = a.[1+Sin(2pt/T)], where a is amplitude or peak value of the sinusoidal wave, T is time period of wave and t is time lapsed. The addition of unity is to make all the terms of the curve positive. The plotted curve is shown below.


 

 

The indicated curve has same amplitude and time-period for each oscillation. Exponential decay is introduced in peak by incorporating exponential term. The governing equation becomes y = a.e(-bt). [1+Sin(2pt/T)], where b is exponential decay factor. A typical representative curve is indicated below for decaying peak of sinusoidal wave.

 

 


 

 

However, the actual curve is not decaying in peak but each subsequent wave has higher peak than the previous wave in current situation. This can be handled by taking a negative value of exponential decay factor. For time compression, the time-period is also assumed to be varying with time, linearly. The same is incorporated in equation and T is replaced by (T-td), where d is time-period decay factor. The produced curve is shown below.

 




The below represented exponential decay and varying time step. If now the mirror image of the curve is taken in y-axis, the designed curve can represent the actual situation of confirmed cases. The curve has reduced peak for each wave and the time period is high for first wave followed by sharp decline for the second wave and so on. This type of equation is used for simulating the curve for daily confirmed cases.

 

 


 

 

Integrated Equation for Waves

The process of equation development is followed for the prediction and the variation of daily confirmed cases is simulated using equation mentioned in previous section. The peak cases is amplified by a factor 4 and the time period is reduced by a factor of 4, as obvious from the used equation. The curve generated is superimposed over the actual number of daily confirmed cases.

 


 

It is clear that curve is representing to a fair degree of accuracy, the daily confirmed cases. As per this, the third wave of curve will follow immediately after end of second wave and probably it rise will be much faster. The peak may be of the order of around 4.74 lakh and the phase may start by 07 June 2021 and end by 29 June 2021. However, if somehow, the lockdown is extended up to 15 June 2021, all over India, the occurrences can be avoided and probably then no third wave will come.

 

Conclusion

As concluding remarks, I would like to reiterate that the daily confirmed cases may be simulated as sinusoidal variation with varying peak and time-period. If mathematics is to be believed, the third wave will be faster and not more severe than second wave. If lockdown is extended till 15 June 2021, the third wave can be avoided. This is a purely mathematical exercise and the assessment needs validation in course of time. I personally don’t see any chances of third wave in India, whether vaccination is complete or incomplete.

 

Stay safe, stay healthy, follow social distancing, and remain connected through social media. All the best.

Regards,

Dr Himanshu Shekhar