Sliding mode control-based analysis of a time-delay HIV dynamic model

Ghamgosar, Mohammad; Mirhosseini-Alizamini, Seyed Mehdi; Farhad, Violet

doi:10.22124/jmm.2026.32402.2937

Sliding mode control-based analysis of a time-delay HIV dynamic model

Articles in Press

Document Type : Research Article

Authors

¹ Academic Center for Education. Cultural and Research (ACCECR), Rasht, Iran.

² Department of Mathematics, Payame Noor University (PNU), Tehran, Iran

³ Department of Mathematics, Payame Noor University (PNU), Tehran, Iran.

10.22124/jmm.2026.32402.2937

Abstract

In this paper, a sliding mode control strategy is developed for a biologically realistic
fourth-order HIV infection model with explicit time delay. The model captures the effects of
intracellular delay and virus production rate on the dynamics of healthy CD4+ T cells, infected cells,
and free viral particles. A sliding mode controller is designed for all system states, and a rigorous
finite-time convergence analysis is provided using Lyapunov theory. It is analytically shown that
the proposed control law guarantees convergence of the system trajectories to the sliding surface in
finite time, despite the presence of time delays and parameter uncertainties. Numerical simulations
conducted under various delay values and virus production rates demonstrate that increasing delay
and viral replication adversely affect system stability and may lead to divergence beyond a critical
delay threshold. In contrast, the proposed controller effectively suppresses oscillations and enforces
rapid convergence of the system states. These results confirm the robustness and effectiveness of
the proposed sliding mode control framework for delayed HIV dynamics.

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Main Subjects