Covid-19 India – what causes first and second wave in India? Understanding the Role of Herd Immunity and double mutant virus.

Covid-19 India – what causes first and second wave in India Understanding the Role of Herd Immunity and double mutant virus.
Figure 1. Daily New Confirmed cases in India


Date: 1st May 2021


First wave

The first Covid 19 wave started back in February 2020 when three students who returned from Wuhan tested positive, however by March the cases began to rise as several people with travel history to affected countries, and their contacts, tested positive. When the cases began to rise, the country went into a lockdown on 25th March till 31st May. The first wave saw its peak on the 16th September (Figure 1) when the daily reported cases were 93,198.


Downward trend of 1st wave

Soon the decline of this wave started after 16th September. This was a gradual coming down making bell curve. This downward slope became a plateau between 1st November 2020  to 25th November 2020, which was actually time of Dussehra/Durga Puja when social distancing norms were flouted by citizens. Soon after Diwali, India again began to see the decline of first wave till 11th Feb with only 11,145 cases. Soon after that the second wave started, but this time with a steeper slope upward.


Reason behind decline of first wave and making bell curve.

We will try to understand the reason purely by analysing the data which is taken from different portals mentioned in the references.

There can be many reasons behind this bell curve in an ongoing pandemic. Every state is different. Their people, their immunity, culture, demographics, connectivity and so many factors are contributing to the numbers of cases. We will discuss here only the major ones, like social distancing, weather, testing and different strain of virus. Let us take each such factor one by one.


Social Distancing

As COVID-19 spread in India, social distancing guidelines were issued by the union and state governments. India open gradually which can be seen from the chart.

Figure 2. Source:
Cell phone mobility data also clearly shows that India gradually opened during the whole year till 20th March 2021, before it again went down after that)


Indian only saw Lockdown phase 1(25 March-14 April), as the strict one, however the total 4 phases of lock down were there till 31st May, however each phase saw restrictions easing down. The Unlock 1.0 to 6.0 process began on 1st June and till 30th November continuously easing down the restriction on social distancing.

The number of cases went down after 16th September, when India was under the process of unlock. This is totally contrary, proving that social distancing cannot be the reason of the first curve downward slope.


Weather: temperature and humidity. 

Various study worldwide has been done to find the role of weather in Covid-19 infection . Research led by The University of Texas at Austin finding that temperature and humidity do not play a significant role in coronavirus spread. There was no indication that a specific type of weather promoted spread over another.

The World Health Organization says the virus can be transmitted in any kind of weather and that there is no reason to believe that cold weather can kill it.


No relationship with testing

Testing cannot be the primary reason of downward slope of the first curve. More than 1.0 million tests were done In between Sept-Dec with only slight fluctuations. In fact, number of tests per confirmed case were increasing during the same period.  Please see figure 3.

Figure 3. Daily new COVID –19 tests in India


The new mutant of Covid-19

There is no such evidence or study that the corona mutated with some new strain and became less infectious during mid of September, so this is also not the primary reason.


Then what is the primary cause?

If we see purely from data point of view the answer is  coming from the concept called “Herd immunity” . Before we prove anything , we first need to understand what is herd immunity and various terms around it.


What is herd immunity?

  • People have heard about it, but most of the people do not understand it. Let’s dig a bit deeper and understand this with the help of some mathematics.
  • Herd immunity is when a large part of population of an area is immune to a specific disease. If enough people are resistant to the cause of a disease, such as virus or bacteria, the disease dies down gradually. When a virus spreads in a community, it cannot affect the 100% of the population.  There will always be people who will never been immunised.  and there is a mathematics behind it.
  • In an ongoing pandemic, we can divide the population in three categories. Susceptible people are those people who have never been infected; Infected people are those people, who are currently infected and can spread the virus; Immune people are those people, who have either got the vaccine or already got infected and recovered.
  • Immune people have developed sufficient immunity, so these people will not be infected again, and will not spread the virus. Infected people will be infecting viruses to susceptible people.
  • There is an important term called “Reproduction Number” or “R Number”.


The basic reproduction number Ro:

The basic reproduction number is defined as the number of cases that are expected to occur on average in a homogeneous population as a result of infection by a single individual, when the population is susceptible at the start of an epidemic, before widespread immunity starts to develop and before any attempt has been made at immunization.

So if one person develops the infection and passes it on to two others, the Ro is 2. If the average Ro in the population is greater than 1, the infection will spread exponentially. If Ro is less than 1, the number of infected people will go down and it will eventually reach to zero. The higher the value of Ro, the faster an epidemic will progress.

The zero in “R zero” means that it is estimated when there is zero immunity in the population, which means the starting point when the disease is started.


Basic reproduction number of different viruses:

Figure 4 : Source

The effective reproduction number Re

The effective reproduction number, Re is the number of people in a population who can be infected by an individual at any specific time. It changes as the population becomes increasingly immunized, either by individual immunity following infection or by vaccination, and also as people die.

When disease starts, Re=Ro, but then as time passes, normally Re will reduce. Re Number can be more than 1, or less than 1. If Re is less than 1, soon disease will die down. Now let’s understand this with an example:

Let us take an example that Re is .9 and there are 100 people infected, they will infect only 100 * .9 = 90 people, who will further infect 90 * .9 = 81 people and so on, reaching the number less than 1, means no further infection.  The herd immunity will be achieved at this point.

If Re is more than 1, as time passes, it will reach 1, and then less than one, and finally we will achieve herd immunity as per above explanation.

Let’s understand as to why Re Number will continuously reduce. The reason is that as the time passes, susceptible people are turning into immune people.

So now when an infected person is spreading virus, the person is meeting susceptible and immune person both. Ratio of susceptible person v/s immune person will always reduce as the time goes. so on an average each infected people meeting susceptible people will also reduce in the same ratio. That means each infected person capacity to infect reduces and hence Re also reduces.

For Example, suppose Ro number of a particular virus is 2.0. In initial days almost complete population is susceptible, with only few infected people and no immune people. Now what will happen?  Every infected person will start infecting other two people and so on and after some time, the number of infected and immune people will be huge. There will be a time when 50% of the susceptible people will turn into immune people.

At this stage the infected person who was infecting two people, now will infect one susceptible and one immune person. So finally the person is infecting only one susceptible person making Re dropped from 2.0 to 1.0.


In this graph called SIR model, [S](t) = susceptible people at time t , [I](t)= infected people at time t, [R](t) = recovered or Immune people at time t. Infected people  first go up and then go down. susceptible people always reduces, but at the end there is a population always non-immune. Recovered/Immune people will always increase but will never reach 100%. We have not taken diseased people in this study to keep it simple.

Herd Immunity Threshold:

This is the point when Re becomes 1, and as a result number of new cases starts going down. the peak is achieved at this point. Please see figure 6, which explains that as Ro increases, % of people required to get herd immunity also increases.

Figure 6

Figure 7


Herd Immunity Threshold (HIT) = 1-1/Ro where Ro = Basis reproduction number
Full Herd Immunity level: S(∞) = 1 − R(∞) = S(0)e−R0R(∞)
Where S(∞) = Susceptible people ratio at the end ; R(∞) = Recovered people ratio at the end ;
S(0) = Susceptible people at starting which will be normally 1 at the starting of epidemic ; Ro = Basic Reproduction Number; e = Euler’s number = 2.7182818284


How does the concept of herd immunity help us in identify the magical slope gradually coming down in the first curve?

We have seen that when we achieve Herd immunity threshold, after that the curve goes down. The same thing happened in India. India achieved “population immunity threshold” around mid of  September, Re became 1.0, and hence the cases started going down.

We are now not using the specific term “Herd Immunity” or “Herd Immunity threshold” now. Instead we will be using the term ‘Population immunity” or “Population immunity threshold”.  the reason is that as per the definition, Herd immunity is achieved when social distancing reached to the “Normal” or “New Normal” level. In our case around mid of September, India was still in partly lock down state, and was still opening up.

So here we would like to introduce a new term “Population Immunity “. The only difference is that Herd immunity is defined when the behaviour of people is normal, with Normal social distancing. However Population immunity is as per the level of current social distancing level which of course would be temporary.

India got population immunity threshold at the level of social distancing of around mid-September and that’s why the curve started going down .

Please see below Re for Covid–19 in India.

Figure8: Effective Reproduction Number Re for Covid-19 in India


R0 of Corona as per Wikipedia is 2.9

It is very difficult to define the exact number of Ro because it depends on many factors, like different strain, geography, culture, density of population etc. which is not constant worldwide.

However, we will not use this number for now, because this number takes the consideration that people are behaving normally and there is no Social distancing. If we see figure 8, Re became stable for some period between 11th June 2020 to 28th July 2020 which is approximately 1.2. This number 1.2 is useful to us. We will consider this as basic reproduction number of population immunity ( we will call it Rpo ) taking social distancing levels of that time

We can see in figure 8 that Re has continuously reduced and reached approximately 1.0 around 16th September 2020. We can also see from Figure 1, that the maximum peak of daily confirmed cases in India were peaking around that time only.

So India has now reached population immunity threshold.  From the Figure 6 after taking Rpe = 1.2, India should have reached a threshold immunity at 16.66 % of population or we can say that approximately 230 million people. And the disease could have completely wiped out at approximately 31.37%  level. Total Confirmed cases till  16th September were 5.02 million. Source: . With this calculation there are 45 times ( 230/5.02 )    estimated cases than confirmed cases. Please note that confirmed cases are those cases which are recorded properly. But there are many times more unreported cases also, that we are calling estimated cases. This number is definitely much more than various published studies on internet. In a Sero survey done, the result was that India had 26-32 times more cases than confirmed cases by 18 Aug 2020.

Further Reproduction Number Re started reducing and started going below 1.0, and so as daily confirmed cases too. On 20th Dec 2020 Re was reduced to .86 (Figure 8) .   and the daily number of confirmed cases went down to approx. 24,500 per day(Figure 1) .

The whole India was relaxed and thought that Corona is gone. However, this was not true.  we can see that second wave came which is   much more dangerous than earlier.


Covid- 19 Second Wave 



Explanation of graph:

Around Feb 11, India touched the bottom with only 1,145 daily confirmed cases. And then suddenly started seeing a rise in cases however the same was not taken into account very seriously and barely any precautions were taken. India crossed 20,000 cases on 12th March and crossed 1,00,000 cases on April 7 which was more than peak of first wave. India crossed 3,00,000 cases on 24rth April making everybody shocked.

We need to again analyse the reason behind this steep curve of second wave. Let us take the same important variables social distancing, testing, and different Covid-19 strain. And see what was the role of these variables behind the second wave.


Social distancing

Let us again see figure 2. There was no any major event happened during mid of February and Social distancing was gradually slowing down. This certainly has some effect on the number of cases every day but we need to really evaluate if this was the primary reason of sudden explosion in the number of cases?



India developed testing capability and was doing approx. 1.0 million testing a day, but when the number of cases reduced the testing was also reduced. when the number was increasing, testing was again ramped up. Testing always followed infection cases but vice versa is not true. So we cannot blame the testing for the cause of second wave.


Actual Culprit: New virus variant. Double Mutant B.1.617

The actual culprit for the second wave is the new virus variant which is minimum  50% more infectious than the earlier one. Having said that it’s reproduction number is also minimum 50% higher. It can also be observed that earlier, 1-2 people were infected in a family however in the second wave it affects the whole family.

While the new variant was the primary reason for the second curve, and the exponential growth, the social distancing easing down worked as a catalyst to further deepen the curve, It is clear that the role of new virus mutant was far more than the role of social distancing in the second curve.

The second wave started and it went upward very fast. In a normal situation it would have again made a sharp bell curve. But now we have strict lock down, which is really effective and this time people are also really scared. This may cause the overall cases to come down till the time lock down again is eased down and people are relaxed.  As the time passes, on one side lock down will be eased down but its effect will be countered on another side as more immunity is developed at community level.


Future? Will there be a third wave?

Nobody wants third wave, but we cannot ignore the risk of it. We cannot ignore the possibility of the more infectious mutant causing herd immunity level to shift further. The third wave will also be dependent to the longevity of the immunity developed in already infected or vaccinated people. Currently we do not know that in how much time this immunity will last. But this time we need to be ready in our research so that we are alarmed much before it happens.


Who wins. Virus or vaccine?

According to the current rate single dose of vaccine has been administered to 113.58 million people across India as of 22nd April and 19.17 million people have received the full doses.

India needs to develop a capacity of giving at least 10 million vaccines a day which seems to be difficult but not impossible.

India is developing herd immunity at slow pace either by getting disease, or by vaccination. Currently there are more estimated infected case than vaccinated people.  Vaccine need to win this race and become primary reason for reaching herd immunity.



Our analysis says that India achieved the population immunity threshold ( Herd immunity with specific social distancing ) around mid of September, based on the strain of virus at that time. However, it was temporary and later around Mid-February a new strain of virus came which was more infectious having more reproduction number causing the population immunity level shift.

In these times of uncertainty, data and numbers can help a lot. Many organisations are working towards the same. The more the data and research we have, the more accuracy we achieve. Future forecasting is the key to plan ahead in advance.



  • We have completely used the data available on public website. We request you to please do not consider this as final model and use only use this blog for reference purposes.
  • There is a very high amount of uncertainty with any model We fully acknowledge the possibility that these results may not reflect reality.
  • If any of the assumptions used to generate these estimates do not hold, then the results may be drastically different.
  • These are the best estimates given what is known at the time this was written, but are subject to change based on new data/evidence.
  • The author is passionate about numbers and is not an epidemiologist, an immunologist.

About the Author: Puneet Mittal is an entrepreneur and an angle investor. He has deep interest in numbers, and analytics.


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