Block-Wise Multi-Objective Binary Control of HIV Treatment: Synchronous and Asynchronous Control Strategies

Bennadja, Islem; Kebiri, Omar; Chaabane, Djamal

doi:10.30473/coam.2026.75678.1341

Articles in Press

Document Type : Research Article

Authors

¹ Laboratory AMCD & RO, Department of Operational Research, Faculty of Mathematics, University of Science and Technology Houari Boumediene (USTHB), Algiers, Algeria

² Department of Stochastics and its Applications, Institute of Mathematics, Brandenburg University of Technology Cottbus-Senftenberg (BTU), Cottbus, Germany

https://doi.org/10.30473/coam.2026.75678.1341

Abstract

Human immunodeficiency virus (HIV) gradually depletes CD4⁺ T-cells, weakening the immune system and potentially leading to AIDS without effective treatment. To counter this immune decline, antiretroviral therapy (ART) has greatly improved the clinical management of HIV by suppressing viral replication and preserving immune function. However, because treatment is often required over long periods, its use may be limited by cumulative toxicity, drug resistance, and adherence challenges. These limitations have encouraged the study of structured treatment interruptions, in which therapy is temporarily stopped and resumed according to a planned schedule to reduce drug exposure while maintaining viral control. In this context, this work proposes a clinically motivated block-wise multi-objective optimization framework for HIV treatment scheduling, based on a nonlinear six-state dynamical model with two binary control variables corresponding to protease inhibitor (PI) and reverse transcriptase inhibitor (RTI) therapies. Rather than determining a single treatment schedule over the entire time horizon, the proposed framework incorporates sequential re-optimization over consecutive 30-day blocks to reflect periodic clinical reassessment and treatment adaptation. The study also compares asynchronous and synchronous binary control strategies under identical conditions. Within each block, daily treatment decisions are optimized using the Non-dominated Sorting Binary Genetic Algorithm II (NSBGA-II), with the aim of preserving CD4⁺ T-cell levels, suppressing viral load, and reducing total drug administration. This formulation provides a more clinically realistic basis for constructing adaptive and personalized HIV treatment schedules.

Highlights

Block-wise multi-objective control framework for HIV treatment optimization.
Daily drug scheduling with NSBGA-II in line with monthly clinical assessments.
Asynchronous vs. synchronous dosing strategies compared for ART regimens.
Pareto-optimal solutions balance immune recovery, drug usage, and stability.
Framework offers adaptive, patient-specific strategies for chronic HIV therapy.

Keywords

Main Subjects

Optimization & Operations Research

References

[1] Ahmed, A., Hill, M., Dong, K.L., Wiseman Ngcobo, M., Zulu, A., Langa, N., Maphalala, L., Pillay, V., MPhil, M.M., Tran, W., Lau, R., Stockman, J.K., Thumbi Ndung’u, I., Karine Dubé, K. (2026). “Stress and coping during an HIV cure-related trial with an analytical treatment interruption: a qualitative assessment of the experiences of young women in Durban, South Africa”. Journal of the International Association of Providers of AIDS Care, 25, 1–17. https://doi.org/10.1177/23259582261423985

[2] Akinsola, V. (2023). “Numerical methods: Euler and Runge–Kutta”. Qualitative and Computational Aspects of Dynamical Systems. https://doi.org/10.5772/ intechopen.108533

[3] Alweshah, M., Jebril, H., Kassaymeh, S., Almiani, M., Alkhalaileh, S., Rjoub, G. (2026). “Optimizing feature selection in cancer microarray data using a heap-driven evolutionary framework for high-dimensional spaces”. Scientific Reports, 16, 6726. https://doi. org/10.1038/s41598-026-37803-5

[4] Coello Coello, C.A., Lechuga, M.S. (2002). “MOPSO: A proposal for multiple objective particle swarm optimization”. Proceedings of the 2002 Congress on Evolutionary Computation (CEC’02), 2, 1051–1056. https://doi.org/10.1109/CEC.2002.1004388

[5] Deb, K., Pratap, A., Agarwal, S., Meyarivan, T. (2002). “A fast and elitist multiobjective genetic algorithm: NSGA-II”. IEEE Transactions on Evolutionary Computation, 6(2), 182–197. https://doi.org/10.1109/4235.996017

[6] Ehrgott, M. (2005). Multicriteria Optimization. Springer Science & Business Media. https://doi.org/10.1007/3-540-27659-9

[7] Hashemi Borzabadi, A., Hasanabadi, M., Sadjadi, N. (2016). “Approximate Pareto optimal solutions of multi-objective optimal control problems by evolutionary algorithms”. Control and Optimization in Applied Mathematics, 1(1), 1–19. https://mathco.journals.pnu.ac.ir/article_2033.html

[8] Kantour, N., Bouroubi, S., Chaabane, D. (2018). “A parallel MOEA with criterion-based selection applied to the knapsack problem”. arXiv preprint arXiv:1811.02271. https://doi.org/10.48550/arXiv.1811.02271

[9] Landi, A., Mazzoldi, A., Andreoni, C., Bianchi, M., Cavallini, A., Laurino, M., Ricotti, L., Iuliano, R., Matteoli, B., Ceccherini-Nelli, L. (2008). “Modelling and control of HIV dynamics”. Computer Methods and Programs in Biomedicine, 89(2), 162–168. https: //doi.org/10.1016/j.cmpb.2007.08.003

[10] Ndung’u, T., Dong, K.L., Colby, D.J., et al. (2026). “Recommendations from the 2nd consensus workshop on analytical treatment interruption in HIV research trials”. The Lancet HIV, 13(4), e271–e281. https://doi.org/10.1016/S2352-3018(25)00373-X

[11] Nuwagaba, J., Li, J.A., Ngo, B., Sutton, R.E. (2025). “30 years of HIV therapy: Current and future antiviral drug targets”. Virology, 603, 110362. https://doi.org/10.1016/ j.virol.2024.110362

[12] Perelson, A.S., Kirschner, D.E., De Boer, R. (1993). “Dynamics of HIV infection of CD4+ T cells”. Mathematical Biosciences, 114(1), 81–125. https://doi.org/10.1016/0025-5564(93)90043-A

[13] Rivadeneira, P.S., Moog, C.H., Stan, G.-B., Costanza, V., Brunet, C., Raffi, F., Ferré, V., Mhawej, M.-J., Biafore, F., Ouattara, D.A. (2014). “Mathematical modeling of HIV dynamics after antiretroviral therapy initiation: a clinical research study”. AIDS Research and Human Retroviruses, 30(9), 831–834. https://doi.org/10.1089/aid. 2013.0286

[14] Salami, D., Koech, E., Turan, J.M., Stafford, K.A., Nyagah, L.M., Ohakanu, S., Ngugi, A.K., Charurat, M. (2026). “Prediction of first and multiple antiretroviral therapy interruptions in people living with HIV: Comparative survival analysis using Cox and explainable machine learning models”. JMIR Medical Informatics, 14(1), e78964. https://doi.org/10.2196/78964

[15] Saravanan, S., Vignesh, R., Rengarajan, S., Vivekanandan, T., Yong, Y.K., Varsha, V., Mounika, P., Sivamalar, S., Vidya, M., Shankar, E.M., Larsson, M., Velu V., Raju, S., Balakrishnan, P., Nisha, B., Venkateswaran, A.R., Kannan, R. (2026). “Negative influence of age and low baseline CD4 on T helper cell recovery among HIV-infected individuals”. Frontiers in Public Health, 14, 1729–1745. https://doi.org/10.3389/fpubh.2026. 1729238

[16] UNAIDS. (2025). “Global HIV & AIDS statistics — Fact sheet”. Joint United Nations Programme on HIV/AIDS. https://www.unaids.org/en/resources/fact-sheet

[17] Vafamand, A., Vafamand, N., Zarei, J., Razavi-Far, R., Saif, M. (2021). “Multi-objective NSBGA-II control of HIV therapy with monthly output measurement”. Biomedical Signal Processing and Control, 68, 102561. https://doi.org/10.1016/j.bspc.2021. 102561

[18] Mio Heinrich, M., Rosenblatt, M., Wieland, F.-G., Stigter, H., Timmer, J. (2025). “On structural and practical identifiability: Current status and update of results”. Current Opinion in Systems Biology, 41, 100546. https://doi.org/10.1016/j.coisb.2025. 100546

[19] Wodarz, D., Nowak, M.A. (1999). “Specific therapy regimes could lead to long-term immunological control of HIV”. Proceedings of the National Academy of Sciences, 96(25), 14464–14469. https://doi.org/10.1073/pnas.96.25.14464

[20] Zhang, Q., Li, H. (2007). “MOEA/D: A multiobjective evolutionary algorithm based on decomposition”. IEEE Transactions on Evolutionary Computation, 11(6), 712–731. https://doi.org/10.1109/TEVC.2007.892759

[21] Ziani, J.S., Silva, G.P.Z., Monteiro, F.L. (2026). “Factors associated with the interruption of antiretroviral therapy in hospitalized people living with HIV: A multivariate analysis”. The Brazilian Journal of Infectious Diseases, 30(1), 104801. https://doi.org/10.1016/j.bjid.2026.104801

[22] Zitzler, E., Laumanns, M., Thiele, L. (2001). “SPEA2: Improving the strength Pareto evolutionary algorithm”. TIK Report, 103, ETH Zurich. https://doi.org/10.3929/ethz-a-004284029

Block-Wise Multi-Objective Binary Control of HIV Treatment: Synchronous and Asynchronous Control Strategies

References

References

Articles in Press, Accepted Manuscript Available Online from 16 June 2026

Articles in Press, Accepted Manuscript
Available Online from 16 June 2026