An Adaptive Lyapunov-Based Controller for HIV Treatment

Document Type : Applied Article


School of Mathematics and Computer Science, Damghan University‎, ‎Damghan‎, ‎Iran.


In view of the tremendous importance of patients’ stability in medical sciences‎, ‎this paper addresses the application of a sliding mode control in medical devices‎. ‎In doing so‎, ‎we consider a nonlinear dynamic system that shows the mathematical model of the human immunodeficiency virus‎. ‎This nonlinear model has three variable states‎: ‎healthy cells‎, ‎infected cells‎, ‎and free viruses‎. ‎The proposed controller displays the effect of medication on preventing the production of the virus and blocking the new infection‎. ‎This controller ensures the stability of this dynamic system provided for HIV in the event of a bounded disturbance‎. ‎The stability and convergence of this process are proved by the Lyapunov theorem‎. ‎Finally‎, ‎a numerical example is given to demonstrate the efficiency of the proposed method.


[1] Aravind B. 2007. “Reverse transcription of the HIV-1 pandemic”, Faseb Journal 21 (14), 3795-808.
[2] Aghajanzadeh O., Sharifi M., Tashakori S., Zohoor H. 2018. “Robust adaptive Lyapunov-based control of hepatitis B infection”, IET systems biology, 12 (2), 62-67.
[3] Barre-Sinoussi F., Chermann J. C., Rey F., Nugeyre M. T., Chamaret S. 1983. “Isolation of T-lymphotropic retrovirus from a patient at risk for acquired immune deficiency syndrome (AIDS)”, Science, (220), 868-871.
[4] Chen Sh. 2021. “Antiretroviral therapy of HIV infection using a novel optimal type-2 fuzzy control strategy”, Alexandria engineering journal, 60 (1), 1545-1555.
[5] Douglas W. B., William A. B., Robert-Guroff M. 1983. “The Human T-Cell Leukemia Lymphoma Virus in the Southeastern United States”, JAMA, 250 (8), 1048-1052.
[6] Friedman-Kien A. E. 1981. “Disseminated Kaposi’s sarcoma syndrome in young homosexual men”, Journal of the American Academy of Dermatology, Dermatol.5, 468-471.
[7] Ghrayeb J., Kato I., McKinney S., Huang J. J., Chanda P. K. 1986. “Human T-Cell Lymphotropic Virus Type III (HTLV-III) Core Antigens: Synthesis in Escherichia coli and Immunoreactivity with Human Sera”, DNA and Cell Biology, 5(2), 93-99.
[8] Kallings L. O. 2008. “The first postmodern pandemic: 25 years of HIV/ AIDS”, Journal of Internal Medicine; 263 (3), 218-243.
[9] Landi A., Mazzoldi A., Andreoni Ch., Bianch M. 2008. “Modelling and control of HIV dynamics”, Computer methods and programs in biomedicine, 89 (2), 162-168.
[10] Markowitz S., edited by William N. Rom. 2007. “Environmental and occupational medicine (4th ed.). Wolters Kluwer/Lippincott Williams & Wilkins”, p. 745.
[11] Moradi H., Sharifi M., Vossoughi G. 2015. “Adaptive robust control of cancer chemotherapy in the presence of parametric uncertainties: A comparison between three hypotheses”, Computers in Biology and Medicine, 56, 145-157.
[12] Sepkowitz K.A. 2001. “AIDS-the first 20 years”, The New England Journal of Medicine 344 (23), 1764-1772.
[13] Sonnabend J., Witkin S. S., Purtilo D. T. 1983. “Acquired immunodeficiency syndrome, opportunistic infections, and malignancies in male homosexuals. A hypothesis of etiologic factors in pathogenesis”, JAMA. 249(17), 2370-2374.
[14] Sharp P. M., Hahn B. H. 2011. “Origins of HIV and the AIDS pandemic”, Cold Spring Harb Perspect Med, 1(1), a006841.
[15] Slotine J. J. E., Li W. 1991. “Applied nonlinear control”, Prentice-Hall, Englewood Cliffs.
[16] Xiaohua X. 2003. “Estimation of HIV/AIDS parameters”, Automatica, 39 (11), 1983-1988.