Fractional-Order Modeling and Stability Analysis of HIV Infection with and Without Antiretroviral Therapy Treatment

Abstract

This article formulates and examines a fractional-order model for Human Immunodeficiency Virus (HIV) infection using Caputo’s derivative in order to model memory-reliant dynamics. The model describes interactions among uninfected, infected, and latently infected CD4⁺ T cells and between free virus particles with and without the effect of Antiretroviral Therapy (ART). We derive major theoretical results of positivity, boundedness, existence, and uniqueness of solutions based on fixed-point theory and fractional calculus. Additionally, we perform a Picard stability analysis, which involves constructing a sequence of successive approximations and proving that small perturbations in initial data lead to proportionally small changes in the solution. We numerically solve the model using Lubich’s convolution quadrature method to simulate its behavior across various fractional orders and ART scenarios. The findings indicate that fractional dynamics are in closer agreement with the chronic characteristics of HIV infection and that ART efficacy increases as a function of increasing order of fractionality, which implies lesser memory effects and faster immune response.