A new optimal control technique for solution of HIV infection model

Malihe Najafi; Hadi Basirzadeh

doi:10.5269/bspm.43220

Malihe Najafi Shahid Chamran University of Ahvaz
Hadi Basirzadeh Shahid Chamran University of Ahvaz

Abstract

In this paper, by means of the optimal control technique and power series technique, we introduce a new method, namely, the optimal control power series technique, by which one can obtain numerical solutions of the HIV infection model of CD4+T cells. The obtained approximate solution has shown good agreement with the experimental results and previous simulations using other methods.

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References

Wang, L., Li, M. Y., Mathematical analysis of the global dynamics of a model for HIV infection of CD4 +T cells, Math. Biosci. 200, 44-57, (2006). https://doi.org/10.1016/j.mbs.2005.12.026

Perelson, A. S., Nelson, P. W., Mathematical analysis of HIV dynamics in vivo, SIAM Rev. 41(1), 3-44, (1999). https://doi.org/10.1137/S0036144598335107

Perelson, A. S., Modeling the interaction of the immune system with HIV, in Mathematical and Statistical Approaches to AIDS Epidemiology, C. Castillo-Chavez, Ed., of Lecture Notes in Biomath, 83 350-370, Springer, Berlin, Germany, 1989. https://doi.org/10.1007/978-3-642-93454-4_17

Asquith, B., Bangham, C. R. M., The dynamics of T-cell fratricide: application of a robust approach to mathematical modelling in immunology, J. Theoret. Biol. 222, 53-69, (2003). https://doi.org/10.1016/S0022-5193(03)00013-4

Nowak, M., May, R., Mathematical biology of HIV infections: antigenic variation and diversity threshold, Math. Biosci. 106, 1-21, (1991). https://doi.org/10.1016/0025-5564(91)90037-J

Ongun, M. Y., The Laplace adomian decomposition method for solving a model for HIV infection of CD4 +T cells, Math. Comput. Model. 53, 597-603, (2011).

Merdan, M., Homotopy perturbation method for solving a model for HIV infection of CD4 +T cells, Istanb. Commerce Uni. J. Sci. 12, 39-52, (2007).

Yuzbası, S., A numerical approach to solve the model for HIV infection of CD4+T cells, Appl. Math. Modell. 36, 5876-5890, (2012). https://doi.org/10.1016/j.apm.2011.12.021

Merdan, M., Gokdogan, A., Yildirim, A., On the numerical solution of themodel for HIV infection of CD4+T cells, Comput. Math. Appl. 62, 118-123, (2011). https://doi.org/10.1016/j.camwa.2011.04.058

Merdan, M., Gokdogan, A., Erturk, V.S., An approximate solution of a model for HIV infection of CD4 +T cells, Iranian J. Sci. Tech. A, 35, 9-12, (2011).

Ghoreishi, M., Ismail, A. I. B. M., Alomari, A. K., Application of the homotopy analysis method for solving a model for HIV infection of CD4+T cells, Math. Compu. Modell. 54, 3007-3015, (2011). https://doi.org/10.1016/j.mcm.2011.07.029

Yuzbası, S. ., Karacayır, M., An exponential Galerkin method for solutions of HIV infection model of CD4 +T-cells, Comp. Bio. Chem. 67, 205-212, (2017). https://doi.org/10.1016/j.compbiolchem.2016.12.006

Srivastava, V.K., Awasthi, M. K., Kumar, S., Numerical approximation for HIV infection of CD4 +T cells mathematical model, Ain Shams Eng. J. 5, 625-629, (2014). https://doi.org/10.1016/j.asej.2013.12.012

Dogan, N., Numerical treatment of the model for HIV infection of CD4 +T cells by using multistep laplace Adomian decomposition method, Discrete Dyn. Nat. Soc., Vol. 2012, Article ID 976352, 11 pages, 2012. https://doi.org/10.1155/2012/976352

Khalid, M., Sultana, M., Zaidi, F., Khan, v, A numerical solution of amodel for HIV infection CD4 +T cells, Int. J. Innov. Sci. Res. 16, 79-85, (2015).

Conway, J. M., Perelson, A.S., Post-treatment control of HIV infection, Proc. Natl. Acad. Sci. U.S.A. 112(17), 5467-5472, (2015). https://doi.org/10.1073/pnas.1419162112

Conway, J. M., Perelson, A.S., Residual viremia in treated HIV+individuals, PLoS Comput. Biol. 12(1), e1004677, (2016). https://doi.org/10.1371/journal.pcbi.1004677

Galloway, N. L., Doitsh, G., Monroe, K. M., Yang, Z., Munoz-Arias, I., Levy, D. N., Greene, W. C., Cell-to-cell transmission of HIV-1 is required to trigger pyroptotic death of lymphoid tissue-derived CD4 +T cells, Cell Rep. 12(10), 1555-1563, (2015). https://doi.org/10.1016/j.celrep.2015.08.011

Luo, J., Wang, W., Chen, H., Fu, R., Bifurcations of a mathematical model for HIV dynamics, J. Math. Anal. Appl. 434, 837-857, (2016). https://doi.org/10.1016/j.jmaa.2015.09.048

Pinto, C. M. A., Carvalho, A. R. M., The role of synaptic transmission in a HIV model with memory, Appl. Math. Comp. 292, 76-95, (2017). https://doi.org/10.1016/j.amc.2016.07.031

Kirk, D. E., Optimal Control Theory, An Introduction, New Jersi, 1970.

Slotine, J. J. E., Li, W., Applied nonlinear control, Prentice Hall, London, 1991.

Mracek, C. P., Cloutier, J.R., Control designs for the nonlinear benchmark problem via the state dependent Riccati equation method, Int. J. Robust Nonlinear Control, 8(45), 401433, 1998. https://doi.org/10.1002/(SICI)1099-1239(19980415/30)8:4/5<401::AID-RNC361>3.0.CO;2-U

Pinch, E. R., Optimal Control and the Calculus of Variations, Oxford University Press, 1993.

Graya, W. S., Espinosa, L.A.D., Thitsa, M., Left inversion of analytic nonlinear SISO systems via formal power series methods, Automatica 50, 2381-2388, (2014). https://doi.org/10.1016/j.automatica.2014.07.017

Sathiyasheela, T., Power series solution method for solving point kinetics equations with lumped model temperature and feedback, Ann. Nuclear Energy, 36, 246-250, (2009). https://doi.org/10.1016/j.anucene.2008.11.005

Momani, S., Arqub, O. A., Hammad, M. A., Abo-Hammour, Z. S., A residual power series technique for solving systems of Initial value problems, Appl. Math. Inf. Sci. 10, 765-775, (2016). https://doi.org/10.18576/amis/100237