Covid vs Mathematics

Inspiration

In 2020, the world faced a pandemic in the form of COVID 19. There have been almost 10 crore infections and 20 lakh people have succumbed to the disease worldwide. Its impact has been felt in every part of our lives whether it be the economy, education or healthcare. Through this project we hope to learn more about the pandemic that we all face with a mathematical approach.

What it does

Our project will look into the vaccination of infectious diseases and how change in various factors impacts the effectiveness of the vaccination program. The factors we aim to study include average human life expectancy, average age at which individuals catch the disease, average age at which individuals are vaccinated against the disease.

How we built it

Through this project we hope to learn more about the pandemic that we all face with a mathematical approach. I would be doing this using Anderson – May model using the concept of Partial Derivatives.

Making the model: As COVID mild cases recover in 14 days, we would the infection period as 14 days. Therefore, the Rate of Recovery, The Rate of Transmission depends on two factors, S and I as it involves the contact between the two. It would be equal to “m*n*I” where m is the average chance of a person getting infected when they come in contact with a susceptible person while n is the average fraction of susceptible people one infected person would likely meet. It will be negative as the susceptible people move to the infected category. Therefore, S’ = -a*I*S persons per day where a is m*n The value of ‘a’ depends on the general health of the population and the level of social interaction. Thus it would change with different group of people. Quarantine directly impacts the value of ‘a’ and helps in reducing it. The final equations for the model are: S’ = -a*I*S I’ = a*I*S – (1/14) *I R’ = (1/14) *I

What we learned

In this project, I learned more about COVID 19, its spread and its vaccination. Also, looked at how mathematical models of real world situations are created. The conversion of a situation into Mathematical equations helps us to estimate and predict the outcome of an event before it actually happens.