Fractional-calculus analysis of human immunodeficiency virus and CD4+ T-cells with control interventions

It is undeniable that HIV infection has been a censorious public health concern over the past four decades. It is reported that HIV is the main reason for AIDs which has decimated the global population of humans and imposed a significant economic burden on affected areas. Hence, it is significant to study the transmission of HIV viruses in the body of a human host. In this study, we use a fractional framework to organise the intricate interactions of CD4⁺ T-cells and HIV viruses in order to investigate HIV infection with control interventions. We apply the operators of Caputo and Atangana–Baleanu to interrogate the transmission phenomena of HIV viruses. For the analysis of our system, we present the basic concepts of the fractional operators. Numerical schemes are provided to show the solution pathways of the system with the variation of input parameters. Furthermore, the findings emphasise the chaotic and dynamical behaviour of HIV. We run several simulations to visualise the influence of input factors and quantitatively illustrated the dynamics of HIV. Chaos and oscillatory behaviour are intimately linked, and this is owing to the system's nonlinearity. Furthermore, our findings indicate the most important factors for infection control and prevention.