You, Covid-19 and Exponentials!
I was talking to my physiologist cousin the other day whose wedding has been fixed on 15th April. I told him to postpone the date as we should prevent arranging and going to as many mass gatherings as we could amidst the current corona outbreak. He was kinda being ignorant saying “We Indians usually don’t get caught to that extent. This is just another buzz. And anyways the big summer is coming, so don’t you worry!” I was laughingly amazed at his confidence and a bit worried at the same time. Let me explain to you why.
What comes to your mind when I tell you that Italy has 27,980 total corona infected cases at the time of writing this article (17th March), active being 23,073. Whereas India has only 137 total cases. So does that mean India is doing a pretty good job at preventing the outbreak? After all, we have the desi cures like cow dung and Gaumutra. But what if we are not exactly preventing it but are just a month behind where Italy is now? Is that shocking enough?
Exactly a month before, Italy had 3 Covid cases. It took them almost a month to lock the country down. Most of the companies in Bengaluru, Pune and NCR have asked their employees to work from home. But in our minds we still have an abstract view about the disease. But with the growth rate, it is hard to keep up with the speed of conversion from abstraction to a real threat.
There comes the power of exponents. Human brains have a hard time comprehending this concept. Notice the pattern: 213, 221, 248, 278, 330, 354, 382, 461, 481, 526, 587, 608, 697, 781, 897 and 999. These are the number of coronavirus cases outside mainland China starting from 3rd February. What would be the next tenth number in this sequence?
Naturally, we just see the difference between the numbers and fail to see the rate. And suddenly when the numbers seem humongous, we get surprised when the sequence was already following the same pattern all along. The next tenth number in the above series was 5365. And in the next 7 days it was 21,395 on March 6th.
Shall we panic? Certainly not. We don’t need the panic but the sincere safety measures which our government has already started taking steps towards. The basic reproduction number or R0 (pronounced R-nought) predicts the number of people who can catch a given bug from a single infected person. For Covid-19, it is 2.2. Meaning a single infected person could likely cause the infection to 2.2 other people.
Why is the government right this time?
From banning visas to enter the country to asking citizens to avoid mass gatherings, the government is doing the best it can to prevent the spread. It’s very simple math actually. If 10 people were already infected in the gathering of 1000, a minimum of 25-30 more people could easily get infected the time they go home (provided infectants are scattered enough). These 30 will cause the spread in their own localities and that is how the exponent builds up. So preventing the world population from shuffling with the countrymen with banning the Visas is really appreciable. But people will still keep shuffling in their local groups.
There does not exist any true exponential curve in any real-world situation. Because sooner or later either we find a total cure or a measure to completely prevent the spread or the whole population gets infected, which is really unlikely.
The real-world curve (in pink) shown above is called a logistic curve. Rather than taking the expected green-colored path, the exponential starts to flatten out after a point which is referred as an inflection point (point C). Before inflection, the number of new cases on any given day will be more than the number of new cases on the previous day. Thus, the growth factor always being > 1. Once the spread crosses the inflection, the number of new cases start to reduce on the subsequent days. Given the current corona pandemic data, we definitely have not crossed the inflection.
As per the above graph from the Corona Tracker Dashboard for India clearly shows that it is at the very early stages of the exponential and seemingly linear.
India has already crossed the stage 1 of the pandemic where majority cases are only the people traveling back from the affected countries a.k.a. imported. At stage 2, the corona starts spreading locally from those people (we are here). Stage 3 is when the disease spreads in the community and the large areas get affected. Stage 4 is where everything breaks down like an emergency with no clear endpoint. Italy and China are here. Recall, Italy had 3 cases on 17th February.
The number of cases India in last 7 days are: 71, 76, 83, 95, 109, 120, 137. And the growth rate being around 7%, 9%, 14%, 15%, 10% and 14%.
WHY and HOW do your efforts matter?
From the sequence stated above, let the average rate of growth be 10%. Assuming we don’t find any quick cure (which is anyways unlikely), the total number of cases in the next 30 days will be –
(1.10)30 x 137 = 2390 cases
And the number of cases in the next 2 months will be –
(1.10)60 x 137 = 9042 cases
Please keep in mind that these are very conservative figures assuming we will still remain on stage 2 and the growth rate will still revolve around 10%.
Now, what will happen when every good citizen starts taking hygienic measures like –
- Washing their hands for at least 20 seconds
- Cough/sneeze in a tissue or elbow
- Avoid public gatherings and Stay Home
Say the rate growth rate drops down to 5% because of the care taken. Then surprisingly the number of possible cases drops down with a greater factor.
(1.05)30 x 137 = 592 cases
(1.05)60 x 137 = 2559 cases
See, your efforts matter!
The number of total cases in South Korea and Italy is 8320 and 27980 whereas the total deaths stand at 81 and 2158 respectively. Noticed something? The number of cases in Italy is 3.5 times more than those of S. Korea but the deaths are more than 26 times. Why is it so?
The main reason is the age of the deceased people. S. Korea is relatively a younger country than Italy. But what does this insight tell us?
We all know that India is a young country where the two-third population is less than 35 years of age, majority living and earning bread & butter from Tier-1 cities. The old population heavily resides in Tier-2, Tier-3 cities/towns and villages. The more people get infected in these areas, the more fatal it would be. The government should try its best to prevent this expansion. On individual levels, we can contribute by limiting our commutes to these towns/villages and taking the above-mentioned measures.
The Good News
Most of the people which you see coughing around are the effects of pollution and dust. Corona is a generic virus and its recovery rate is also exponential. It might be life-threatning to old people for their low immunity and aging effects.
There is absolutely no need to create any panic as some TV channels are constantly keep on doing. Just do your bit of contribution, follow authentic news, know what spreads the virus and what doesn’t and let’s all hope to hit the point C as soon as possible!!
This post was inspired by Grant Sanderson’s video. Check out his channel for more amazing thing: