A Fractional Perspective on the Dynamics of HIV, Considering the Interaction of Viruses and Immune System with the Effect of Antiretroviral Therapy

Abstract

HIV infection is a worldwide health threat, necessitating a multifaceted strategy that includes prevention, testing, treatment and care. Moreover, it is essential to address the structural and social factors that influence the spread of this viral infection. In this study, we utilize fractional calculus to clarify the dynamics of HIV infection in vivo, specifically examining the interface amid the HIV and the immune system and taking into account the impact of antiretroviral therapy. We use important results from fractional theory to analyze our proposed model of HIV infection and developed a numerical scheme to depict the system’s dynamic behavior. By varying input factors, we were able to observe the system’s chaotic nature and track its trajectory, as well as examine the effect of viruses on T-cells. Our results reveal key factors affecting the system, and demonstrate the consequence of antiretroviral therapy on our proposed model of HIV. Moreover, we observe that the system’s strong non-linearity is responsible for the oscillation phenomena and identify the most sensitive parameters of the system.