Qualitative analysis of a novel HIV infection model of macrophage cells in Caputo fractional environment

In this paper, we propose a novel mathematical model of HIV infection that focuses on the role of macrophage cells. We rigorously analyze the model’s properties, including boundedness, non-negativity and existence of a unique solution, to ensure its biological relevance. We identify the possible steady states and calculate the basic reproduction number, [Formula: see text], which helps determine the conditions for disease persistence or clearance. Both local and global stabilities of the steady states are examined analytically and numerically. We employ a combination of methods, including stability analysis, sensitivity analysis of each parameter with respect to basic reproduction number [Formula: see text] and numerical simulations using the Fractional Forward Euler method, to explore the impact of varying fractional-order ([Formula: see text]) on the system. The results show that variations in the fractional-order ([Formula: see text]) lead to significant changes in describing disease progression or digression, the behavior of equilibrium points, stability conditions and the existence of bifurcations. Our study reveals that that increased memory effect slower the disease progression. It also interpreted with biological insights, highlighting the implications of fractional-order modeling in understanding HIV dynamics. This novel approach offers fresh perspectives on the control of HIV. In addition, this work contributes a novel perspective to modeling HIV dynamics by incorporating fractional-order differential equations and presents a more comprehensive approach compared to previous integer-order models. It provides new insights into the application of fractional calculus in biological modeling, particularly in the field of infectious diseases. The paper concludes with a discussion of the key findings and their potential applications.