Global Stability of a Delayed HIV Model Incorporating Cytokine Effects and Impaired Immune Responses

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DOI: https://doi.org/10.28924/2291-8639-23-2025-264
Published: Oct 29, 2025
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N. H. AlShamrani, Global Stability of a Delayed HIV Model Incorporating Cytokine Effects and Impaired Immune Responses, Int. J. Anal. Appl., 23 (2025), 264.

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N. H. AlShamrani

Abstract

A mathematical model describing HIV infection influenced by inflammatory cytokines and weakened adaptive immune responses is formulated and analyzed. The system is represented by delay differential equations that characterize the interactions among uninfected CD4+T cells, infected CD4+T cells, inflammatory cytokines, HIV particles, cytotoxic T lymphocytes (CTLs), and antibodies. The model incorporates three forms of distributed delays: (i) a delay associated with the infection of healthy CD4+T cells, (ii) a delay representing the activation of cytokine responses, and (iii) a delay corresponding to the maturation period of new HIV virions. The model’s biological plausibility is verified by demonstrating essential properties of the solutions, including their non-negativity and ultimate boundedness. The basic reproduction number, R0, is computed and serves as a threshold parameter governing the existence and stability of the system’s equilibrium points. Global stability of both equilibrium states is rigorously analyzed through the construction of Lyapunov functionals. To confirm the analytical results, numerical experiments are carried out, accompanied by a sensitivity study of R0 to examine how variations in essential parameters affect the system. The impact of increased impairment of the adaptive immune response, as well as the delay time, on the progression of viral activity within the body has been discussed. Our findings indicate that, the greater the impairment in adaptive immune response, the more the virus progresses within the body, worsening the patient’s condition. Conversely, an increase in the delay time leads to suppression of viral growth.

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