Modelling of COVID-19 Using Fractional Differential Equations

TL;DR

This paper develops a fractional differential equation-based extension of the SEIQRDP model to analyze COVID-19 transmission, emphasizing the roles of PPE and social distancing, and tests its accuracy against Canadian data.

Contribution

It introduces a fractional differential equation approach to extend the SEIQRDP model for COVID-19, incorporating additional factors like quarantine and insusceptibility.

Findings

Fractional model fits Canadian COVID-19 data well.

Social distancing significantly reduces disease spread.

PPE effectiveness is highlighted in controlling transmission.

Abstract

In this work, we have described the mathematical modeling of COVID-19 transmission using fractional differential equations. The mathematical modeling of infectious disease goes back to the 1760s when the famous mathematician Daniel Bernoulli used an elementary version of compartmental modeling to find the effectiveness of deliberate smallpox inoculation on life expectancy. We have used the well-known SIR (Susceptible, Infected and Recovered) model of Kermack & McKendrick to extend the analysis further by including exposure, quarantining, insusceptibility and deaths in a SEIQRDP model. Further, we have generalized this model by using the solutions of Fractional Differential Equations to test the accuracy and validity of the mathematical modeling techniques against Canadian COVID-19 trends and spread of real-world disease. Our work also emphasizes the importance of Personal Protection Equipment (PPE) and impact of social distancing on controlling the spread of COVID-19.