Sensitivity and optimal control analysis of HIV/AIDS model with two different stages of infection subpopulation
Authors
U. Habibah
- Department of Mathematics and member of Research Group of Biomathematics, Brawijaya University, Jl. Veteran Malang, Indonesia.
Trisilowati
- Department of Mathematics and member of Research Group of Biomathematics, Brawijaya University, Jl. Veteran Malang, Indonesia.
Y. L. Pradana
- Undergraduate student of the Department of Mathematics, Brawijaya University, Jl. Veteran Malang, Indonesia.
Abstract
We study optimal control analysis of HIV/AIDS model with two different stages of infection subpopulation. There are two controls, antiretroviral (ARV) treatment is given to HIV-infected subpopulation, and HAART (highly active antiretroviral treatment) is given to full-blown AIDS subpopulation. Before that, we analyze the sensitivity of parameters which can be used to determine the most parameter take effect in the spread of HIV virus. We apply the sensitivity analysis to all the parameters appear in the reproduction number. Furthermore, we apply optimal control theory to minimize HIV-infected and full-blown AIDS subpopulation, and the cost related to the implementation of control strategies using the Pontryagin's Minimum Principle. We prove an existence of a optimal control pair. Numerical solution is conducted by solving the optimally system using the sweep backward and forward method. The results show that giving control pair in the model can decrease the infected and the full-blown AIDS subpopulations significantly.
Share and Cite
ISRP Style
U. Habibah, Trisilowati, Y. L. Pradana, Sensitivity and optimal control analysis of HIV/AIDS model with two different stages of infection subpopulation, Journal of Mathematics and Computer Science, 26 (2022), no. 1, 90--100
AMA Style
Habibah U., Trisilowati, Pradana Y. L., Sensitivity and optimal control analysis of HIV/AIDS model with two different stages of infection subpopulation. J Math Comput SCI-JM. (2022); 26(1):90--100
Chicago/Turabian Style
Habibah, U., Trisilowati,, Pradana, Y. L.. "Sensitivity and optimal control analysis of HIV/AIDS model with two different stages of infection subpopulation." Journal of Mathematics and Computer Science, 26, no. 1 (2022): 90--100
Keywords
- Optimal control
- HIV/AIDS model
- Pontryagin's minimum principle
MSC
References
-
[1]
W. Assawinchaichote, Robust $H_\infty$ Controller Design for Nonlinear Positive HIV/AIDS Infection Dynamic Model: A Fuzzy Approach, Proc. Int. MultiConf. Eng. Comput. Sci., I (2012), 5 pages
-
[2]
L. M. Cai, S. L. Guo, S. P. Wang, Analysis of an extended HIV/AIDS epidemic model with treatment, Appl. Math. Comput., 236 (2014), 621--627
-
[3]
L. M. Cai, X. Z. Li, M. Ghosh, B. Z. Guo, Stability analysis of an HIV/AIDS epidemic Model with treatment, J. Comput. Appl. Math., 229 (2009), 313--323
-
[4]
N. Chitnis, J. M. Hyman, J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70 (2008), 1272--1296
-
[5]
H. R. Erfanian, M. H. Noori Skandari, Optimal Control of an HIV Model, J. Math. Comput. Sci., 2 (2011), 650--658
-
[6]
U. Habibah, R. A. Sari, Optimal control analysis of HIV/AIDS epidemic model with an antiretroviral treatment, Aust. J. Math. Anal. Appl., 17 (2020), 11 pages
-
[7]
U. Habibah, R. A. Sari, The Effectiveness of an Antiretroviral Treatment (ARV) and a Highly Active Antiretroviral Theraphy (HAART) on HIV/AIDS Epidemic Model, AIP Conference Proceedings, 2021 (2018), 12 pages
-
[8]
U. Habibah, Trisilowati, Y. L. Pradana, W. Villadistyan, Mathematical model of HIV/AIDS with two different stages of infection subpopulation and its stability analysis, Eng. Lett., 29 (2020), 13 pages
-
[9]
H.-F. Huo, R. Chen, Stability of an HIV/AIDS Treatment Model with Different Stages, Discrete Dyn. Nat. Soc., 2015 (2015), 9 pages
-
[10]
H.-F. Huo, R. Chen, X.-Y. Wang, Modelling and Stability of HIV/AIDS Epidemic Model with Treatment, Appl. Math. Model., 40 (2016), 6550--6559
-
[11]
S. Khajanchi, D. Ghosh, The Combined Effects of Optimal Control in Cancer Remission, Appl. Math. Comput., 271 (2015), 375--388
-
[12]
S. Lenhart, J. T. Workman, Optimal Control Applied to Biological Models, Chapman & Hall/CRC, Boca Raton (2007)
-
[13]
D. L. Lukes, Differential Equations: Clasical to controlled, Academic Press, New York (1982)
-
[14]
M. Marsudi, N. Hidayat, R. B. E. Wibowo, Application of Optimal Control Strategies for the Spread of HIV in a Population, Res. J. Life Sci., 4 (2017), 9 pages
-
[15]
M. Najariyan, M. H. Farahi, M. Alavian, Optimal Control of HIV Infection by using Fuzzy Dynamical Systems, J. Math. Comput. Sci., 2 (2011), 639--649
-
[16]
S. I. Oke, M. B. Matadi, S. S. Xulu, Optimal Control Analysis of a Mathematical Model for Breast Cancer, Math. Comput. Appl., 23 (2018), 28 pages
-
[17]
M. A. Rois, T. Trisilowati, U. Habibah, Local Sensitivity Analysis of COVID-19 Epidemic with Quarantine and Isolation using Normalized Index, Telematika, 14 (2021), 13--24
-
[18]
S. Saha, G. P. Samanta, Modelling and Optimal Control of HIV/AIDS prevention through PrEP and Limited Treatment, Phys. A, 516 (2019), 280--307
-
[19]
T. Trisilowati, Mathematical Modelling of Tumor Growth and Interaction with Host Tissue and the Immune System, PhD thesis, Mathematical Sciences School, Queensland University of Technology (2012)
-
[20]
B. Ulfa, T. Trisilowati, W. M. Kusumawinahyu, Dynamical Analysis of HIV/AIDS Epidemic Model with Treatment, J. Exp. Life Sci., 8 (2018), 11 pages
-
[21]
S. Mushayabasa, C.P. Bhunu, Modeling HIV Transmission Dynamics among Male prisoners in Sub-Saharan Africa, IAENG Inter. J. Appl. Math., 41 (2011), 6 pages