Estimate the number of actual COVID-19 positive people in India as of today.

Approach:

1. Identify the no. of international travellers entering India every day

2. Identify the total no. of infected people out of this population

3. Identify the average contacts made by an infected person in a day and newly infected people because of this person

4. Identify the total infected people because of the new arrivals, new contacts made and disease tranmission rate before lockdown and social distancing happened

5. Identify the total infected people by April 27th (after social distancing)

6. Identify the total no. of positive cases by April 27th (Would be lesser since symtoms start appearing after 14 days)

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1. Identify the no. of international travellers entering India every day

There are 30 international airports in India with 7 major ones including Delhi, Mumbai, Chennai, Kochi, Bangalore, Hyderabad, Kolkata. 
Delhi Airport receives around 800-2200 international passengers during lean and peak hours every day which makes amounts to a total of 30000 (~1200*24 hours) international passengers everyday. 
So, total no. of international passengers entering India everyday could be estimated at 1 lakh per day.
(Delhi - 30K, Mumbai - 20K, Chennai - 15K, Kochi - 10K, Bangalore - 8 K, Hyderabad - 6 K, Kolkata - 5 K and so on..)

2. Identify the total no. of infected people out of this population

Assuming the infected ratio to be 1% (taking into consideration the worldwide disease spread % which is not very high), the total no. of positive cases on the first day = 1000 people

3. Identify the average contacts made by an infected person in a day and newly infected people because of this person

Depending on the lifestyle of the person, contacts made by a person can vary from 5 to 50 people on an average with median standing at 10 people. 
Assuming the disease transmission rate to be 1% (As the no. of positive cases doubles every 10th day), new people getting infected by one infected person everyday would be .1 people on an average

4. Identify the total infected people because of the new arrivals, new contacts made and disease tranmission rate before lockdown and social distancing happened

Day 1 - C =  1000 positive cases - X1
Day 2 - X1 + X1*.1 + W2 = X1*1.1 + C = 1000*1.1 + 1000 = 2100 positive cases - X2
Day 3 - X2 + X2*.1 + W3 = X2*1.1 + C = 2100*1.1 + 1000 = 3310 positive cases - X3
and so on...
So total no. of infected people by March 20th (Before social distancing and lockdown happened) would be 1163909 ~ 11 Lakh infected people

5. Identify the total infected people by April 27th

Assuming that after the lockdown and social distancing the transmission rate reduced to .01% from .1% and since international travel was stopped, there were no new cases coming from international travel.
So, total no. of infected people by April 27th (37 days) would be 1522635 ~ 15 lakh infected people

6. Identify the total no. of positive cases by April 27th

Total no. of positive cases by April 27th would be the total no. of infected people by April 13th (since it takes 14 days before any symptoms appear)
so total no. of positive cases by April 27th would be 1324636 ~ 13 lakh positive cases

So, total no. of positive cases in India by April 27th would be 13 lakh.  
 

Assumptions: There is no real way to find the actual initial no. of affected cases, as lots of cases may not be reported. Hence, I’m estimating on the basis of people probably affected then drilling down further to see the total estimated cases-

Equation: No. of people in India * contact rate * % of people contracting through contact.

 Where,

• Contact rate = Avg no. of people who’d probably be affected through contact  (% of people who’ll be in contact/ person)
• % of people contracting though contact= Not all people who are in contact with covid-19 positive will contract the disease, hence this metric measures the probability of actual disease contraction

 Total population of India= 1.3B

 Inorder to calculate contact rate, defining Population by where they live-

Without social distancing:

 Thus, total infected due to not following social distancing could be 320.15MM people.

However, due to rigorous social distancing measures taken by India, my assumption is that only 20 % of the actual population calculated may be affected= 0.2*320.15MM ~64MM people.