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Numerical Methods of Lyapunov Control Function (LCF) for De-replication of Dual HIV-Pathogen Infections
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Volume 6, 2018
Issue 1 (March)
Pages: 1-10   |   Vol. 6, No. 1, March 2018   |   Follow on         
Paper in PDF Downloads: 26   Since Jun. 14, 2018 Views: 932   Since Jun. 14, 2018
Bassey Echeng Bassey, Department of Mathematics / Statistics, Cross River University of Technology, Calabar, Nigeria.
Bassey Delphine Rexson, Department of Botany, University of Calabar, Calabar, Nigeria.
In this study, among other control measures for the control of human immune deficiency virus (HIV), the intense of this paper were conditioned to incorporate a novel Lyapunov control function (LCF) for the control of nonlinear dual HIV-pathogen infectivity and maximization of the concentration of healthy cytotoxic lymphocytes (CD4+ T cell count) model. The uncertainty surrounding the gradual decay in the state variable parameters and the external control setting was studied. This was followed with the application of system derived novel LCF at varying strategies. Predominantly, the strategies considered are the inputs into the infected cells and to the dual infectious virions (viral load and pathogen) stages. Realistic comparison between control strategies were drawn and explicit evaluation of the system dynamics with the introduction of considerable noise to the dual infectious virions conducted. The result that followed from numerical simulations presented an incredible appreciation of the effectiveness of the nonlinear control for the maximization of health CD4+ T cells count with tremendous suppression of dual virions at a considerable systemic cost. Therefore, the simplicity and application of this model is self-commendable for the elimination of other related co-infectious diseases.
Lyapunov-Control-Function, De-Replication, Dual-Virions, Co-Infectious-Diseases, Microscopically-Indistinguishable, Globally-Asymptomatic
Alazabi, F. A. and Zohdy, M. A. (2012) Nonlinear Uncertainty HIV-1 Controller by Using Control Lyapunov Function. IJMNTA, 1, 33-39.
Bortz, D. M. and Nelson, P. W. (2004) Sensitivity Analysis of a Nonlinear Lumped Parameter Model of HIV Infection Dynamics. Bulletin of Mathematical Biology, 66, 5, 1009-1026.
Bassey, E. B. and Lebedev, K. A. (2016) On Analysis of Parameter Estimation Model for the Treatment of Pathogen-Induced HIV Infectivity. Open Access Library Journal, 3 (4): 1-13.
Xia, X. (2003) Estimation of HIV/AIDS Parameters. Automatica, 39, 1983-1988.
Perelson, A. S. and Nelson, P. W. (1999) Mathematical Analysis of HIV-1 Dynamics in Vivo. Society for Industrial and Applied Mathematics Review, 41, 1, 3- 44. doi: 10.1137/S0036144598335107
Ouattara, D. A. (2005) Mathematical Analysis of the HIV-1 Infection: Parameter Estimation, Therapies Effectiveness and Therapeutical Failures. Proceedings of the 2005 IEEE, Engineering in Medicine and Biology 27th Annual Conference, Shanghai, 1-4 September 2005, 821-824.
Stilianakis, N. I., Dietz, K. and Schenzle D. (1997) Analysis of a Model for the Pathogenesis of AIDS. Mathematical Bio-sciences, 145, 1, 27-46. doi: 10.1016/S0025-5564(97)00018-7
Wei, X., Ghosh, S. K., Taylor, M. E., Johnson, V. A., Emini, E. A., Deutsch, P. and Lifson, J. D. (1995) Viral Dynamics.
in HIV-1 Infection. Nature, 273, 117-122. http://dx.doi.org/10.1038/373117a0
Perelson, A. S., Neumann, A. U., Markowitz, M., Leonard, J. M. and Ho, D. D. (1996) HIV-1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell Lifespan, and Viral Generation Time. Science, 271, 5255, 1582-1586. doi: 10.1126/science.271.5255.1582
Shirazian, M. and Farahi, M. H. (2010) Optimal Control Strategy for a Fully Determined HIV Model. Intelligent Controland Automation, 1, 15-19. http://dx.doi.org/10.4236/ica.2010.11002
Badakhshan, K. P. and Kamyad, A. V. (2007) Numerical Solution of Nonlinear Optimal Control Problems Using Nonlinear Programming. Applied Mathematics and Computation, 187, 1511-1519.
Baasey, B. E. (2017) Quantitative Approximability of Optimal Control by Linear Programing Model for Asymptomatic Dual HIV - Pathogen Infections. International Journal of Scientific and Innovative Mathematical Research, vol. 5, no. 9, p. 01-21, 2017. http://dx.doi.org/10.20431/ 2347-3142.0509001
Joshi, H. R. (2002) Optimal Control of an HIV Immunology Model. Optimal Control Applications and Methods, 23: 199-213.
Baasey, E. (2017) On Optimal Control Pair Treatment: Clinical Management of Viremia Levels In Pathogenic-Induced HIV-1 Infections. Biomed J Sci & Tech Res 1 (2) 1-9. BJSTR. MS.ID.000204
Praly, L. and Wang, Y. (1996) Stabilization in Spite of Matched Un-Modeled Dynamics and an Equivalent Definition of Input-to-State Stability. Mathematics of Control, Signals and Systems, 9, 1, 1-33. doi: 10.1007/BF01211516
Sepulchre, R., Jankovic, M. and Kokotovic, P. (1997) Constructive Nonlinear Control. Springer-Verlag, Berlin.
Faubourg, L. and Pomet, J. (1999) Design of Control Lyapunov Functions for ‘Jurdjevic-Quinn’ Systems. Stability and Stabilization of Nonlinear Systems, 246, 137-150. doi: 10.1007/1-84628-577-1_7
Gregio, J. M., Caetano, M. A. L. and Yoneyama, T. (2009) State Estimation and Optimal Long Period Clinical Treatment of HIV Seropositive Patients. Anais da Academic Brasileira de Ciencias, 81, 3-12.
Knorr, A. and Srivastava, R. (2004) Evaluation of HIV-1 Kinetic Models using Quantitative Discrimination Analysis. Bio-informatics, 21, 8, 1668-1677. doi: 10.1093/bioinformatics/bti230
Bacciotti, A. (1992) Local Stabilizability of Nonlinear Control Systems. World Scientific, Singapore.
Wein, L. M., Zenois, S. A. and Nowak, M. A. (1997) Dynamic Modeling Therapies for HIV: A Control Theoretic Approach. J. Theor. Biol., 185, 15-29.
Adams, B. M., Banks, H. T., Hee-Dae K. and Tran, H. T. (2004) Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches.
http://citeseerx.ist.psu.edu/viewdoc/summary?doi= Accessed February 16, 2018.
Bassey E. Bassey (2017) Optimal control model for immune effectors response and multiple chemotherapy treatment (MCT) of dual delayed HIV - pathogen infections. SDRP Journal of Infectious Diseases Treatment & Therapy, 1 (1) 1-18.
Korobeinikov, A. (2004) Global Properties of Basic Virus Dynamics Models. Bulletin of Mathematical Biology, 66, 4, 2004, 879-883. doi: 10.1016/j.bulm.2004.02.001
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