A robust study to conceptualize the interactions of CD4+ T-cells and human immunodeficiency virus via fractional-calculus

Abstract

It is eminent that the infection of HIV is a censorious problem to public health for the last forty years. This viral infection is the cause of Acquired Immunodeficiency Virus (AIDS) which deteriorated the human population around the world and having a high economic burden on different infected regions. In HIV infection, the virus attack on the CD4+ T-cells in the body, this viral infection makes the body of the host open for the attack of other infections. Therefore, it is valuable to study and examine the interactions of CD4+ T-cells and HIV viruses for a better understanding of the infection. In this study, we structure the intricate interactions of HIV and CD4+ T-cells through the fractional framework to interrogate this viral infection. We use Atangana-Baleanu (AB) fractional operator to highlight the overall picture of HIV infection with the nonlocal and nonsingular kernel. We present the fundamental theory of the fractional operator for the analysis of our system. We have proved results for the unique solution of the AB system of HIV infection. A numerical method is introduced to highlight the chaotic and dynamical behavior of the HIV infection with the variation of the input parameters. We perform different simulations to conceptualize the role of input factor on the system and highlight the dynamics of HIV infection through numerically. The chaos and oscillatory behavior is strongly associated and is due to the nonlinearity of the system. In addition to this, our analysis recommends the most dominant parameters for the control and prevention of the infection.