A Fractional-Order Compartmental Model of Vaccination for COVID-19 with the Fear Factor

During the past several years, the deadly COVID-19 pandemic has dramatically affected the world; the death toll exceeds 4.8 million across the world according to current statistics. Mathematical modeling is one of the critical tools being used to fight against this deadly infectious disease. It has been observed that the transmission of COVID-19 follows a fading memory process. We have used the fractional order differential operator to identify this kind of disease transmission, considering both fear effects and vaccination in our proposed mathematical model. Our COVID-19 disease model was analyzed by considering the Caputo fractional operator. A brief description of this operator and a mathematical analysis of the proposed model involving this operator are presented. In addition, a numerical simulation of the proposed model is presented along with the resulting analytical findings. We show that fear effects play a pivotal role in reducing infections in the population as well as in encouraging the vaccination campaign. Furthermore, decreasing the fractional-order parameter a value minimizes the number of infected individuals. The analysis presented here reveals that the system switches its stability for the critical value of the basic reproduction number R-0 = 1.

Automated summary

This article presents a method for analyzing the transmission of COVID-19 using mathematical modeling, considering fear effects and vaccination. They identify this type of disease transmission using fractional order differential operator and conduct mathematical analysis and numerical simulation. The results show that fear effects and reducing the fractional order parameter can reduce the number of infections.