A new optimal control technique for solution of HIV infection model
DOI:
https://doi.org/10.5269/bspm.43220Abstract
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.
References
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18. 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
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21. Kirk, D. E., Optimal Control Theory, An Introduction, New Jersi, 1970.
22. Slotine, J. J. E., Li, W., Applied nonlinear control, Prentice Hall, London, 1991.
23. 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
24. Pinch, E. R., Optimal Control and the Calculus of Variations, Oxford University Press, 1993.
25. 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
26. 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
27. 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
2. 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
3. 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
4. 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
5. 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
6. 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).
7. 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).
8. 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
9. 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
10. 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).
11. 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
12. 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
13. 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
14. 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
15. 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).
16. 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
17. 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
18. 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
19. 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
20. 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
21. Kirk, D. E., Optimal Control Theory, An Introduction, New Jersi, 1970.
22. Slotine, J. J. E., Li, W., Applied nonlinear control, Prentice Hall, London, 1991.
23. 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
24. Pinch, E. R., Optimal Control and the Calculus of Variations, Oxford University Press, 1993.
25. 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
26. 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
27. 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
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2021-12-17
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