# Mathematics in Covid-19

**Table of Contents**

1. | Introduction |

2. | Spread of COVID-19 |

3. | How well do people transmit the disease? |

4. | Conclusion |

### July 30, 2020

**Reading Time: 2 minutes**

**Introduction**

Understanding the growth of corona virus is largely about numbers. Therefore, mathematical epidemiology is playing a crucial role in the fight against this infectious disease. With basic mathematical ideas, researchers can forecast the progression of this disease and understand the intervention on the disease spread to stop the pandemic.

As it is always said, **“nature has all the answers”**.

A small sapling may grow into a beautiful tree in years. This tree will have branches leading to a beautiful structure of tree with leaves and flowers blooming from it. So,** branching** in trees is the arrangement and position of the branches on a tree which gives the tree a definite shape.

**Spread of COVID-19**

Let us understand the spread of Covid-19 using few mathematical concepts, one out of which is the **Tree growth** in gardening.

A **binary tree **is used to understand the same. A binary tree is a tree structure in which it has a base node and each node has at most two or more nodes.

**Exponential growth** is a specific way that a quantity may **increase** over time. It happens when the instantaneous rate of change of a quantity changes with respect to time proportionally to the quantity itself.

Let us understand this concept with an example of **tree growth** in gardening showing how the virus spreads.

If each infected person ends up infecting **two or three** new people, then we’ll have more and more infections everyday and the virus will spread very **quickly.**

** **

Another important concept is **linear growth.** It is detected as the growth by the **same amount** each time step.

Let us take an example of linear growth to show the virus spread using binary tree growth concept.

If each person just infects **one** new person, then the virus will spread very **slowly** and in a manageable way where we can control the spread of it.

Here’s a quick video to give an idea about the virus spread in exponential growth and linear growth.

So, if we reduce the spread of Covid-19 to an extent, that is when an infected person will infect 0.5 new people, then the average number of infections will be 0.5 and there is a 50% chance that they will infect one new person and a 50% chance that they will infect no new person.

Hence, the next question would be:

**How well do people transmit the disease?**

That’s called the** ****“Reproductive number”** or **R _{0}**. It is the number of new people who contract the virus on average from an infected person. It depends on how easily the germ jumps from person to person.

It also matters how many people are infected and how long are they actually contagious. **R _{0}** only matters at the beginning of an outbreak.

From the tree growth concept, we learned that the **R _{0}=2 or 3**, the disease grows

**exponentially**and when

**R**, the disease grows

_{0}=1**linearly**.

**Conclusion**

Apart from the spread of this deadly virus, we are all in this pandemic together. We can help each other from not spreading this disease by following a few steps like maintaining social distance, keeping ourselves hygienic and wearing masks. So** Stay home, Stay safe!**

**“PREVENTION IS BETTER THAN CURE”**