Caputo Fractional Derivative for Analysis of COVID-19 and HIV/AIDS Transmission

Abstract

In this study, Caputo fractional derivative model of HIV and COVID-19 infections is analyzed. Moreover, the well-posedness of a model is verified to depict that the developed model is mathematically meaningful and biologically acceptable. Particularly, Mittag Leffler function is incorporated to show that total population size is bounded whereas fixed point theory is applied to show the existence and uniqueness of solution of the constructed Caputo fractional derivative model of HIV and COVID-19 infections. The study depicts that as the order of fractional derivative increase the size of the infected variable decrease as time increase. Additionally, memory effects correspond to order of derivative in the reduction of a number of populations infected both with HIV and COVID-19 infections. Numerical simulations are performed using MATLAB platform.