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An Optimal Control Strategy for Antiretroviral Treatment of HIV Infection in Presence of Immunotherapy

  • Jyoti Nath, Bhagya [3] ; Kumar Sarmah, Hemanta [1] ; Maurer, Helmut [2]
    1. [1] Gauhati University

      Gauhati University

      India

    2. [2] University of Münster

      University of Münster

      Kreisfreie Stadt Münster, Alemania

    3. [3] Barnagar College
    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
  • Idioma: inglés
  • DOI: 10.1007/s12346-022-00564-3
  • Enlaces
  • Resumen

    • Human immunodeficiency virus infection destroys immune system of an HIV infected individual, which results in the risk of other life threatening diseases such as kidney disease, liver disease, diabetes and some types of cancer. To date, there is no cure of this infectious disease, however, there exist antiretroviral drugs which help an HIV infected individual to live a quality life. But, these antiretroviral drugs are costly and have different side effects. Recent studies indicate that immunotherapy can be used in addition to these antiretroviral drugs for better management of HIV infection. In this study, we consider an HIV infection model incorporating the effects of antiretroviral drugs and immunotherapy. We verify that the model solutions are non-negative and bounded in the feasible domain. Stability analysis of HIV infection-free equilibrium point indicates that HIV is eradicated for a basic reproduction number less than one. In order to maximize healthy CD4+ T cells with minimum cost and side effects of drugs, we propose an optimal control problem with two different objectives. The optimal control problems are solved using discretization and large-scale optimization methods. We obtain optimal treatment strategies for antiretroviral drugs and immune boosting drugs.

  • Referencias bibliográficas
    • 1. Ahr, B., Robert-Hebmann, V., Devaux, C., Biard-Piechaczyk, M.: Apoptosis of uninfected cells induced by HIV envelope glycoproteins. Retrovirology...
    • 2. Betts, J.T.: Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, Advances in Control and Design, vol. 19....
    • 3. Ciupe, M.S., Bivort, B.L., Bortz, D.M., Nelson, P.W.: Estimating kinetic parameters from HIV primary infection data through the eyes of...
    • 4. Coddington, E.A., Levinson, N.: Theory of Ordinary Differential Equations. Tata McGraw-Hill Education, New York (1955)
    • 5. Danane, J., Meskaf, A., Allali, K.: Optimal control of a delayed hepatitis B viral infection model with HBV DNA-containing capsids and...
    • 6. Denizot, M., Varbanov, M., Espert, L., Robert-Hebmann, V., Sagnier, S., Garcia, E., Curriu, M., Mamoun, R., Blanco, J., Biard-Piechaczyk,...
    • 7. Douek, D.C., Brenchley, J.M., Betts, M.R., Ambrozak, D.R., Hill, B.J., Okamoto, Y., Casazza, J.P., Kuruppu, J., Kunstman, K., Wolinsky,...
    • 8. Driessche, P.V., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibra for compartmental models of disease transmission....
    • 9. Embretson, J., Zupancic, M., Ribas, J.L., Burke, A., Racz, P., Racz, K.T., Haase, A.T.: Massive covert infection of helper T lymphocytes...
    • 10. Fleming, W.H., Rishel, R.W.: Deterministic and Stochastic Optimal Control. Springer, New York (1975)
    • 11. Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL: A Modeling Language for Mathematical Programming. Duxbury Press, Brooks-Cole Publishing...
    • 12. Frydas, A., Leptokaridou, E., Partsanakis, E., Kourklidou, M., Sarantopoulos, A.: Emerging therapies in HIV infection: is the immune response...
    • 13. Garg, H., Mohl, J., Joshi, A.: HIV-1 induced bystander apoptosis. Viruses 4, 3020–3043 (2012)
    • 14. Geng, Y., Xu, J.: Stability and bifurcation analysis for a delayed viral infection model with full logistic proliferation. Int. J. Biomath....
    • 15. Göllmann, L., Maurer, H.: Theory and applications of optimal control problems with multiple timedelays. J. Ind. Manag. Optim. 10, 413–441...
    • 16. Gougeon, M.L., Colizzi, V., Dalgleish, A., Montagnier, L.: New concepts in AIDS pathogenesis. AIDS Res. Hum. Retrovir. 9, 287–289 (1993)
    • 17. Grossman, Z., Meier-Schellersheim, M., Sousa, A.E., Victorino, R.M., Paul, W.E.: CD4+ T cell depletion in HIV infection: are we closer...
    • 18. Gumel, A.B., Shivakumar, P.N., Sahai, B.M.: A mathematical model for the dynamics of HIV-1 during the typical course of infection. Nonlinear...
    • 19. Gupta, P.K., Dutta, A.: A mathematical model on HIV/AIDS with fusion effect: analysis and homotopy solution. Eur. Phys. J. Plus 134, 265...
    • 20. Gupta, P.K., Dutta, A.: Numerical Solution with analysis of HIV/AIDS Dynamics model with effect of fusion and cure rate. Numer. Algebra...
    • 21. Hager, W.W.: Runge–Kutta methods in optimal control and the transformed adjoint system. Numer. Math. 87, 247–282 (2000)
    • 22. Hattaf, K., Yousfi, N.: Two optimal treatments of HIV infection model. World J. Model. Simul. 8(1), 27–35 (2012)
    • 23. Hattaf, K., Rachik, M., Saadi, S., Yousfi, N.: Optimal control of treatment in a basic virus infection model. Appl. Math. Sci. 3(20),...
    • 24. Kariuki, S.M., Musyoki, S.K., Kemoi, E.K.: Immunotherapeutic treatment of HIV-1: review of safety and efficacy. Int. J. Cur. Res. Rev....
    • 25. LaSalle, J.P.: The stability of dynamical systems. In: Regional Conference Series in Applied Mathematics. SIAM, Philadelaphia (1976)
    • 26. Lee, E.B., Markus, L.: Foundations of Optimal Control. John Wilea Inc, New York (1967)
    • 27. Lukes, D.L.: Differential Equations: Classical to Controlled, Mathematics in Science and Engineering, p. 162. Academic Press, New York,...
    • 28. McCune, J.M.: The dynamics of CD4+ T-cell depletion in HIV disease. Nature 410, 974–979 (2001)
    • 29. Ogunlaran, O.M., Noutchie, S.C.O.: Mathematical model for an effective management of HIV infection. BioMed Res. Int. 2016, 4217548 (2016)....
    • 30. Pawelek, K.A., Liu, S., Pahlevani, F., Rong, L.: A model of HIV-1 infection with two time delays: mathematical analysis and comparison...
    • 31. Poonia, B.: Immunotherapy in HIV infection. J. Infect. Dis. Ther. (2013). https://doi.org/10.4172/ 2332-0877.1000102
    • 32. Pontryagin, L., Boltyanskii, V., et al.: The Mathematical Theory of Optimal Processes. Wiley, New York (1962)
    • 33. Shamsara, E., Afsharnezhad, Z., Effati, S.: Optimal drug control in a four-dimensional HIV infection model. Optim. Control Appl. Methods...
    • 34. Silva, C.J., Maurer, H.: Optimal control of HIV treatment and immunotherapy combination with state and control delays. Optim. Control...
    • 35. Srivastava, P.K., Chandra, P.: Modeling the dynamics of HIV and CD4+ T cells during primary infection. Nonlinear Anal. Real World...
    • 36. Vanham, G., Van Gulck, E.: Can immunotherapy be useful as a “functional cure” for infection with human immunodeficiency virus-1? Retrovirology...
    • 37. Wächter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming....
    • 38. World Health Organization. https://www.who.int/news-room/fact-sheets/detail/hiv-aids. Accessed 20 July 2021
    • 39. World Health Organization: Interim WHO Clinical Staging of HIV/AIDS and HIV/AIDS Case Definitions for Surveillance: African Region (2005)....
    • 40. Willems, J.L.: Stability Theory of Dynamical Systems. Wiley, New York (1970)
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