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On Analysis of Parameter Estimation Model for the Treatment of Pathogen-Induced HIV Infectivity

DOI: 10.4236/oalib.1102603, PP. 1-13

Subject Areas: Mathematical Analysis, Numerical Mathematics, Ordinary Differential Equation

Keywords: Asymptomatic-Stage, De-Replication, Discretization, Infectivity, Mutation-Ability

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Abstract

Multiplicity of new cases of HIV/AIDS and its allied infectious diseases daunted by lack of proper parametric estimation necessitated this present work. Formulated using ordinary differential equation was a five-dimensional (5D) differential mathematical model with which compatibility of optimal control strategy for dual (viral load and parasitoid-pathogen) infectivity in the blood plasma was investigated. Discretization method indicated the incompatibility of the model due to large error derivatives. The study using numerical method established treatment set point with which we explored the variation of predominant model parameters and thereof investigated the maximization of uninfected healthy CD4 T cell count as well as the de-replication of viruses following the consistent administration of reverse transcriptase inhibitor from set point. Presented was a series of numerical calculations obtained using well-known Runge-Kutter of order of precision 4, in Mathcad platform. Analysis of simulated parameters showed that distortion of replication viruses and de-transmutation of susceptible CD4 T cells by viruses via chemotherapy led to restoration and gradual increase of healthy blood plasma, with near zero declination of both viral load and parasitoid-pathogen within chemotherapy validity time frame. The model was worthy in the study of treatment analysis of dual HIV—pathogen infection and thereof recommended for other related dual infectious diseases.

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Bassey, B. E. and Andreyevich, L. K. (2016). On Analysis of Parameter Estimation Model for the Treatment of Pathogen-Induced HIV Infectivity. Open Access Library Journal, 3, e2603. doi: http://dx.doi.org/10.4236/oalib.1102603.

References

[1]  Shirazian, M. and Farahi, M.H. (2010) Optimal Control Strategy for a Fully Determined HIV Model. Intelligent Control and Automation, 1, 15-19.
http://dx.doi.org/10.4236/ica.2010.11002
[2]  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
[3]  Nowak, M.A. and Bangham, C.R.M. (1996) Population Dynamics of Immune Responses to Persistent Viruses. Science, 272, 74-79.
http://dx.doi.org/10.1126/science.272.5258.74
[4]  Xia, X. (2003) Estimation of HIV/AIDS Parameters. Automatica, 39, 1983-1988.
http://dx.doi.org/10.1016/S0005-1098(03)00220-6
[5]  Xia, X. (2007) Modelling of HIV Infection: Vaccine Readiness, Drug Effectiveness and Therapeutical Failures. Journal of Process Control, 17, 253-260.
http://dx.doi.org/10.1016/j.jprocont.2006.10.007
[6]  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.
http://dx.doi.org/10.1016/j.amc.2006.09.074
[7]  Grégio, J.M., Caetano, M.A.L. and Yoneyama, T. (2009) State Estimation and Optimal Long Period Clinical Treatment of HIV Seropositive Patients. Anais da Academia Brasileira de Ciências, 81, 3-12.
http://dx.doi.org/10.1590/S0001-37652009000100002
[8]  Wein, L.M., Zenios, S.A. and Nowak, M.A. (1997) Dynamic Multidrug Therapies for HIV: A Control Theoretic Approach. Journal of Theoretical Biology, 185, 15-29.
http://dx.doi.org/10.1006/jtbi.1996.0253
[9]  Badakhshan, K.P., Kamyad, A.V. and Azemi, A. (2007) Using AVK Method to Solve Nonlinear Problems with Uncertain Parameters. Applied Mathematics and Computation, 189, 27-34.
http://dx.doi.org/10.1016/j.amc.2006.11.172
[10]  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.
[11]  Ho, D.D., Neumann, A.U., Perelson, A.S., Chen, W., Leonard, J.M. and Markowitz, M. (1995) Rapid Turnover of Plasma Virions and CD4 Lymphocytes in HIV-1 Infection. Nature, 273, 123-126.
http://dx.doi.org/10.1038/373123a0
[12]  Bassey, B.E. and Lebedev, K.A. (2015) On Mathematical Model of the Impact of Verimia Levels and Condom Use: Preventive Measures for the Spread of HIV/AIDS. Proceedings of XVIII-th International Scientific Conference Modern Science: Actual Problems and Ways of Their Solution”, Lipetsk, 20 July 2015, Ed. by M. Y. Levin, Lipetsk: OOO Max Information Technology. 18, 5, 47-56. (In Russian)
[13]  Bassey, B.E. and Lebedev, K.A. (2015) On the Mathematical Modeling of the Impact of Numerical Stability of the Treatment of Vertical Transmitted HIV/AIDS Infections. Proceedings of XVI-th International Scientific ConferenceScientific Potential of Contemporary Russia”, Lipetsk, 10 August 2015, Ed. by M. Y. Levin, Lipetsk: OOO Max Information Technology. 16, 5, 7-19. (In Russian)
[14]  Bassey, B.E. and Lebedev, K.A. (2015) On Global Convergence and Impact of Multistageand Pade Techniques for Iterative Methods in Nonlinear HIV/AIDS Preventive Chain Model. Proceedings of the XIX-th International Scientific ConferenceModern Science: Current Problems and Solutions”, Lipetsk, 14 September 2015, Ed. By M. Levin, Lipetsk: LLC Maximal Information Technologies. 19, 6, 17-27. (In Russian)
[15]  Wikipedia (2015) The Free Encyclopedia, Immune System.
https://en.wikipedia.org/wiki/Immune_system/
[16]  Pattman, R., Snow, M., Handy, P., Sankar, K.N. and Elawad, B. (2005) Oxford Handbook of Genitourinary Medicine, HIV and AIDS. Oxford University Press, USA.
[17]  Fister, K.R. and Lenhart, S. (1998) Optimizing Chemotherapy in an HIV Model. Journal of Differential Equations, 1998, 1-12.
[18]  Joshi, H.R. (2002) Optimal Control of an HIV Immunology Model. Optimal Control Applications and Methods, 23, 199-213.
http://dx.doi.org/10.1002/oca.710
[19]  Kirschner, D. and Webb, G.F. (1998) Immunotherapy of HIV-1 Infection. Journal of Biological Systems, 6, 71-83.
http://dx.doi.org/10.1142/S0218339098000091
[20]  Butler, S., Kirschner, D. and Lenhart, S. (2016) Optimal Control of Chemotherapy Affecting the Infectivity of HIV.
http://www.nacad.ufrj.br/~amit/opt_infect_HIV_kirsch.pdf

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