Math & Beyond

Mathematics of Covid-19

July 31, 2020

Reading Time: 3 minutes

Introduction

Mathematicians world-wide are contributing to the understanding of the Covid-19 epidemic. Mathematics plays an essential role in fighting COVID-19, which is why the pandemic has featured a lot on Plus. 

Here in this Blog, I’m explaining the global view growth of the Novel Corona Virus (Covid-19) through Yeast production in terms of Mathematical concepts.


Yeast Growth in Baking 

The baker's yeast is commercially produced on a nutrient source that is rich in sugar (usually molasses: a by-product of the sugar refining). The fermentation is conducted in large tanks. Once the yeast fills the tank, it is harvested by centrifugation, giving an off-white liquid known as cream yeast.

Yeast growth in baking

As you all know, yeast is a teeny tiny creature that helps in production of bread. But, one interesting thing about yeast is, it doubles every single day.

For a better visual explanation watch this video:

Let’s imagine now there’s exactly one yeast in the jar.

Jar

Then, the next day there will be two yeast in the jar. 

jar 2

If the jar remains closed then, on the third day there will be four yeast in the jar.

jar 3

Can you guess how many yeast will be there on the fourth day inside the jar? Yes, exactly there will be 8 yeast inside the jar.

jar 4

If this process is carried out for the next 25-30 days the jar will be filled with full of yeast. It’s a baker's dream come true.

This process of growing where the number of yeast doubles every day is an example of exponential growth, which was exactly the growth that the Doctors were noticing with the number of coronavirus patients.

For a better visual explanation, watch this video.

early warning of covid-19


Is Exponential growth and linear growth both the same?

No, Exponential growth is fundamentally different from linear growth.

Linear growth is what happens when the quality increases by the same amount every time. For example, when I’m preparing my bread for delivery, I carry two loaves of bread to my car. So, the number of loaves in my car goes from Zero to two, to four, to six, to eight and to ten. Now that is a slow steady linear growth.

For a better visual explanation, watch this video:

linear growth

For the better understanding of the exponential growth I would suggest you to click this video and to follow the instructions of the baker. 

So imagine a jar with a thousand yeast in it. On the next day, the jar is filled with 2000 yeast. Similarly, on the third day with 4000 yeast and on the fourth day the jar is filled with 8000 yeast.

Now here’s a question to you, if a jar is completely full on the 30th day then on which day would the yeast fill them halfway?

For a better visual explanation watch this video:

So, the answer to the above question is, the jar is half-filled on the 29th day. Most of you guys would’ve thought of an answer as 15th day.

jar 5

The solution to the above question is explained visually in this video.

Jar 6

Here’s a most amazing thing about exponential growth is that for any fixed amount of time, the multiplication factor is fixed.

As we have discussed the yeast doubling every 24hrs. If the yeast doubles every 24 hours then, what happens every 48 hours?

It is simply that the number of yeast will double twice or in other words multiplied by 4. In fact, any 48 hour time period will quadruple the number of yeast. When the growth is exponential any fixed time will multiply the yeast with any fixed amount. 

Here’s a visual explanation: 

For a better understanding of linear growth I would like you to watch this video and follow the baker instructions. 


Conclusion

Don’t let the virus multiply like yeast.
At this tough time it is important for all of us to maintain social distancing and to follow the rules and regulations issued by the government and WHO. Wash your hands for a minimum of 30 seconds and maintain a minimum of 4 meter distance with another person while talking. 

Stay Home! Stay Safe!
 

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