Typesetting math: 100%
Search Advanced

Mathematical Biosciences and Engineering

2004, Volume 1, Issue 2: 223-241. doi: 10.3934/mbe.2004.1.223
Previous Article Next Article

Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches

  • 1.
    Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695
  • 2.
    Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212
  • Accepted: 29 June 2018 Published: 01 July 2004

  • MSC : 34H05, 37M05, 49K15, 65L05, 92B05, 92C60.

  • We formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits drug ''cocktail'' therapies. We derive HIV therapeutic strategies by formulating and analyzing an optimal control problem using two types of dynamic treatments representing reverse transcriptase (RT) inhibitors and protease inhibitors (PIs). Continuous optimal therapies are found by solving the corresponding optimality systems. In addition, using ideas from dynamic programming, we formulate and derive suboptimal structured treatment interruptions (STI) in antiviral therapy that include drug-free periods of immune-mediated control of HIV. Our numerical results support a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy.

    Citation: B. M. Adams, H. T. Banks, Hee-Dae Kwon, Hien T. Tran. Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches[J]. Mathematical Biosciences and Engineering, 2004, 1(2): 223-241. doi: 10.3934/mbe.2004.1.223

    Related Papers:

    [1] Divya Thakur, Belinda Marchand . Hybrid optimal control for HIV multi-drug therapies: A finite set control transcription approach. Mathematical Biosciences and Engineering, 2012, 9(4): 899-914. doi: 10.3934/mbe.2012.9.899
    [2] Divine Wanduku . A nonlinear multi-population behavioral model to assess the roles of education campaigns, random supply of aids, and delayed ART treatment in HIV/AIDS epidemics. Mathematical Biosciences and Engineering, 2020, 17(6): 6791-6837. doi: 10.3934/mbe.2020354
    [3] Gordon Akudibillah, Abhishek Pandey, Jan Medlock . Optimal control for HIV treatment. Mathematical Biosciences and Engineering, 2019, 16(1): 373-396. doi: 10.3934/mbe.2019018
    [4] Dan Shi, Shuo Ma, Qimin Zhang . Sliding mode dynamics and optimal control for HIV model. Mathematical Biosciences and Engineering, 2023, 20(4): 7273-7297. doi: 10.3934/mbe.2023315
    [5] Youyi Yang, Yongzhen Pei, Xiyin Liang, Yunfei Lv . An optimal scheme to boost immunity and suppress viruses for HIV by combining a phased immunotherapy with the sustaining antiviral therapy. Mathematical Biosciences and Engineering, 2020, 17(5): 4578-4608. doi: 10.3934/mbe.2020253
    [6] Seyedeh N. Khatami, Chaitra Gopalappa . A reinforcement learning model to inform optimal decision paths for HIV elimination. Mathematical Biosciences and Engineering, 2021, 18(6): 7666-7684. doi: 10.3934/mbe.2021380
    [7] Federico Papa, Francesca Binda, Giovanni Felici, Marco Franzetti, Alberto Gandolfi, Carmela Sinisgalli, Claudia Balotta . A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment. Mathematical Biosciences and Engineering, 2018, 15(1): 181-207. doi: 10.3934/mbe.2018008
    [8] Yu Ji . Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Mathematical Biosciences and Engineering, 2015, 12(3): 525-536. doi: 10.3934/mbe.2015.12.525
    [9] Damilola Olabode, Libin Rong, Xueying Wang . Optimal control in HIV chemotherapy with termination viral load and latent reservoir. Mathematical Biosciences and Engineering, 2019, 16(2): 619-635. doi: 10.3934/mbe.2019030
    [10] Arni S. R. Srinivasa Rao, Kurien Thomas, Kurapati Sudhakar, Philip K. Maini . HIV/AIDS epidemic in India and predicting the impact of the national response: Mathematical modeling and analysis. Mathematical Biosciences and Engineering, 2009, 6(4): 779-813. doi: 10.3934/mbe.2009.6.779
  • We formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits drug ''cocktail'' therapies. We derive HIV therapeutic strategies by formulating and analyzing an optimal control problem using two types of dynamic treatments representing reverse transcriptase (RT) inhibitors and protease inhibitors (PIs). Continuous optimal therapies are found by solving the corresponding optimality systems. In addition, using ideas from dynamic programming, we formulate and derive suboptimal structured treatment interruptions (STI) in antiviral therapy that include drug-free periods of immune-mediated control of HIV. Our numerical results support a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy.


  • This article has been cited by:

    1. Esteban A. Hernandez-Vargas, Dhagash Mehta, Richard H. Middleton, Towards Modeling HIV Long Term Behavior, 2011, 44, 14746670, 581, 10.3182/20110828-6-IT-1002.00685
    2. Yinggao Zhou, Kuan Yang, Kai Zhou, Chunling Wang, Optimal Treatment Strategies for HIV with Antibody Response, 2014, 2014, 1110-757X, 1, 10.1155/2014/685289
    3. Chao Yu, Yinzhao Dong, Jiming Liu, Guoqi Ren, Incorporating causal factors into reinforcement learning for dynamic treatment regimes in HIV, 2019, 19, 1472-6947, 10.1186/s12911-019-0755-6
    4. Hybrid optimal control for HIV multi-drug therapies: A finite set control transcription approach, 2012, 9, 1551-0018, 899, 10.3934/mbe.2012.9.899
    5. Hassan Zarei, Ali Vahidian Kamyad, Sohrab Effati, Multiobjective Optimal Control of HIV Dynamics, 2010, 2010, 1024-123X, 1, 10.1155/2010/568315
    6. A. M. Elaiw, Global properties of a class of virus infection models with multitarget cells, 2012, 69, 0924-090X, 423, 10.1007/s11071-011-0275-0
    7. Hegagi Mohamed Ali, Ismail Gad Ameen, Save the pine forests of wilt disease using a fractional optimal control strategy, 2020, 132, 09600779, 109554, 10.1016/j.chaos.2019.109554
    8. B. M. Adams, H. T. Banks, M. Davidian, E. S. Rosenberg, Estimation and Prediction With HIV-Treatment Interruption Data, 2007, 69, 0092-8240, 563, 10.1007/s11538-006-9140-6
    9. Yunjeong Lee, Yoon-gu Hwang, Hee-Dae Kwon, Jun Yong Choi, Jeehyun Lee, Hierarchical Mixed-Effects Model for HIV Dynamics, 2020, 80, 0036-1399, 1290, 10.1137/19M1246031
    10. Lucian Busoniu, Damien Ernst, Bart De Schutter, Robert Babuska, Cross-Entropy Optimization of Control Policies With Adaptive Basis Functions, 2011, 41, 1083-4419, 196, 10.1109/TSMCB.2010.2050586
    11. Marie-José Mhawej, Claude H. Moog, Federico Biafore, Cécile Brunet-François, Control of the HIV infection and drug dosage, 2010, 5, 17468094, 45, 10.1016/j.bspc.2009.05.001
    12. Cameron J. Browne, Sergei S. Pilyugin, Minimizing R0 for in-host virus model with periodic combination antiviral therapy, 2016, 21, 1531-3492, 3315, 10.3934/dcdsb.2016099
    13. Dayse H. Pastore, Roberto C. A. Thomé, Claudia M. Dias, Edilson F. Arruda, Hyun M. Yang, A model for interactions between immune cells and HIV considering drug treatments, 2018, 37, 0101-8205, 282, 10.1007/s40314-017-0528-8
    14. Gabriel Otieno, Joseph Koske, John Mutiso, Cost Effectiveness Analysis of Optimal Malaria Control Strategies in Kenya, 2016, 4, 2227-7390, 14, 10.3390/math4010014
    15. Kazeem O. Okosun, Ouifki Rachid, Nizar Marcus, Optimal control strategies and cost-effectiveness analysis of a malaria model, 2013, 111, 03032647, 83, 10.1016/j.biosystems.2012.09.008
    16. Hee-Dae Kwon, Jeehyun Lee, Myoungho Yoon, An age-structured model with immune response of HIV infection: Modeling and optimal control approach, 2014, 19, 1553-524X, 153, 10.3934/dcdsb.2014.19.153
    17. G. Bocharov, V. Chereshnev, I. Gainova, S. Bazhan, B. Bachmetyev, J. Argilaguet, J. Martinez, A. Meyerhans, Human Immunodeficiency Virus Infection : from Biological Observations to Mechanistic Mathematical Modelling, 2012, 7, 0973-5348, 78, 10.1051/mmnp/20127507
    18. Youping Yang, Yanni Xiao, Ning Wang, Jianhong Wu, Optimal control of drug therapy: Melding pharmacokinetics with viral dynamics, 2012, 107, 03032647, 174, 10.1016/j.biosystems.2011.11.011
    19. GBENGA JACOB ABIODUN, NIZAR MARCUS, KAZEEM OARE OKOSUN, PETER JOSEPH WITBOOI, A MODEL FOR CONTROL OF HIV/AIDS WITH PARENTAL CARE, 2013, 06, 1793-5245, 1350006, 10.1142/S179352451350006X
    20. Siriwan Chankan, Rachata Thienchai, Weera Yukunthorn, Control Theory for HIV Dynamics: Sliding Mode Control in Antiviral Drug Therapy, 2018, 1144, 1742-6588, 012070, 10.1088/1742-6596/1144/1/012070
    21. Yanni Xiao, Hongyu Miao, Sanyi Tang, Hulin Wu, Modeling antiretroviral drug responses for HIV-1 infected patients using differential equation models, 2013, 65, 0169409X, 940, 10.1016/j.addr.2013.04.005
    22. Mingwang Shen, Yanni Xiao, Libin Rong, Lauren Ancel Meyers, Conflict and accord of optimal treatment strategies for HIV infection within and between hosts, 2019, 309, 00255564, 107, 10.1016/j.mbs.2019.01.007
    23. O. Krakovska, L. M. Wahl, Costs versus benefits: best possible and best practical treatment regimens for HIV, 2007, 54, 0303-6812, 385, 10.1007/s00285-006-0059-1
    24. Ferrante Neri, Jari Toivanen, Raino A. E. Mäkinen, An adaptive evolutionary algorithm with intelligent mutation local searchers for designing multidrug therapies for HIV, 2007, 27, 0924-669X, 219, 10.1007/s10489-007-0069-8
    25. Abdulfatai A. Momoh, Armin Fügenschuh, Optimal control of intervention strategies and cost effectiveness analysis for a Zika virus model, 2018, 18, 22116923, 99, 10.1016/j.orhc.2017.08.004
    26. Soyoung Kim, Aurelio A. de los Reyes, Eunok Jung, Mathematical model and intervention strategies for mitigating tuberculosis in the Philippines, 2018, 443, 00225193, 100, 10.1016/j.jtbi.2018.01.026
    27. K.O. Okosun, Rachid Ouifki, Nizar Marcus, Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity, 2011, 106, 03032647, 136, 10.1016/j.biosystems.2011.07.006
    28. Yufan Zhao, Michael R. Kosorok, Donglin Zeng, Reinforcement learning design for cancer clinical trials, 2009, 28, 02776715, 3294, 10.1002/sim.3720
    29. Chittaranjan Mondal, Debadatta Adak, Nandadulal Bairagi, Optimal control in a multi-pathways HIV-1 infection model: a comparison between mono-drug and multi-drug therapies, 2019, 0020-7179, 1, 10.1080/00207179.2019.1690694
    30. Aivar Sootla, Guy-Bart Stan, Damien Ernst, 2020, Chapter 11, 978-3-030-35712-2, 283, 10.1007/978-3-030-35713-9_11
    31. Tobias Jung, Louis Wehenkel, Damien Ernst, Francis Maes, Optimized look-ahead tree policies: a bridge between look-ahead tree policies and direct policy search, 2014, 28, 08906327, 255, 10.1002/acs.2387
    32. H T Banks, Sarah Grove, Shuhua Hu, Yanyuan Ma, A hierarchical Bayesian approach for parameter estimation in HIV models, 2005, 21, 0266-5611, 1803, 10.1088/0266-5611/21/6/001
    33. Hee-Dae Kwon, Optimal treatment strategies derived from a HIV model with drug-resistant mutants, 2007, 188, 00963003, 1193, 10.1016/j.amc.2006.10.071
    34. Matthias Haering, Andreas Hördt, Michael Meyer-Hermann, Esteban A. Hernandez-Vargas, Computational Study to Determine When to Initiate and Alternate Therapy in HIV Infection, 2014, 2014, 2314-6133, 1, 10.1155/2014/472869
    35. Lucian Busoniu, Remi Munos, Bart De Schutter, Robert Babuska, 2011, Optimistic planning for sparsely stochastic systems, 978-1-4244-9887-1, 48, 10.1109/ADPRL.2011.5967375
    36. Milad Moradi, Reza Shahnazi, Ali Chaibakhsh, Individual-based multi-objective optimal structured treatment interruption for HIV infection, 2019, 85, 15684946, 105780, 10.1016/j.asoc.2019.105780
    37. Seidu Baba, I Daabo Mohammed, S Bornaa Christopher, Endemic analysis of HIV/AIDS transmission in the presence of antiretroviral therapy, 2016, 8, 2141-2359, 44, 10.5897/JAHR2016.0377
    38. Bashir Abdullahi Baba, Bulent Bilgehan, Optimal control of a fractional order model for the COVID – 19 pandemic, 2021, 144, 09600779, 110678, 10.1016/j.chaos.2021.110678
    39. Marios M. Hadjiandreou, Raul Conejeros, D. Ian Wilson, Long-term HIV dynamics subject to continuous therapy and structured treatment interruptions, 2009, 64, 00092509, 1600, 10.1016/j.ces.2008.12.010
    40. Kazeem Oare Okosun, Oluwole Daniel Makinde, On a drug-resistant malaria model with susceptible individuals without access to basic amenities, 2012, 38, 0092-0606, 507, 10.1007/s10867-012-9269-5
    41. H. Chang, C. H. Moog, A. Astolfi, 2014, Analysis of the HIV eradication phenomenon at the early stage of infection with an extracellular deterministic model, 978-1-4244-7929-0, 330, 10.1109/EMBC.2014.6943596
    42. Yazdan Batmani, Hamid Khaloozadeh, On the design of human immunodeficiency virus treatment based on a non‐linear time‐delay model, 2014, 8, 1751-8857, 13, 10.1049/iet-syb.2013.0012
    43. H. Chang, A. Astolfi, 2007, Immune response’s enhancement via controlled drug scheduling, 978-1-4244-1497-0, 3919, 10.1109/CDC.2007.4434462
    44. MAGNO ENRIQUE MENDOZA MEZA, AMIT BHAYA, VIRUS DYNAMICS MODELS SUBJECTED TO A HYBRID ON-OFF CONTROL, 2010, 18, 0218-3390, 339, 10.1142/S0218339010003287
    45. Lucian Busoniu, Remi Munos, Elod Pall, 2014, An analysis of optimistic, best-first search for minimax sequential decision making, 978-1-4799-4552-8, 1, 10.1109/ADPRL.2014.7010615
    46. E. Bonyah, M.A. Khan, K.O. Okosun, J.F. Gómez‐Aguilar, On the co‐infection of dengue fever and Zika virus, 2019, 40, 0143-2087, 394, 10.1002/oca.2483
    47. H. T. Banks, M. Davidian, Shuhua Hu, Grace M. Kepler, E. S. Rosenberg, Modelling HIV immune response and validation with clinical data, 2008, 2, 1751-3758, 357, 10.1080/17513750701813184
    48. H. T. Banks, Shuhua Hu, Taesoo Jang, Hee-Dae Kwon, Modelling and optimal control of immune response of renal transplant recipients, 2012, 6, 1751-3758, 539, 10.1080/17513758.2012.655328
    49. H. Kheiri, M. Jafari, Fractional optimal control of an HIV/AIDS epidemic model with random testing and contact tracing, 2019, 60, 1598-5865, 387, 10.1007/s12190-018-01219-w
    50. Taesoo Jang, Hee-Dae Kwon, Jeehyun Lee, Free Terminal Time Optimal Control Problem of an HIV Model Based on a Conjugate Gradient Method, 2011, 73, 0092-8240, 2408, 10.1007/s11538-011-9630-z
    51. Joo-Won Lee, Nam Hoon Jo, Hyungbo Shim, Young Ik Son, On the Stability of Critical Point for Positive Systems and Its Applications to Biological Systems, 2013, 8, 1975-0102, 1530, 10.5370/JEET.2013.8.6.1530
    52. Iman Hajizadeh, Mohammad Shahrokhi, Observer-Based Output Feedback Linearization Control with Application to HIV Dynamics, 2015, 54, 0888-5885, 2697, 10.1021/ie5022442
    53. H. T. Banks, Ariel Cintrón-Arias, Franz Kappel, 2013, Chapter 3, 978-3-642-32881-7, 43, 10.1007/978-3-642-32882-4_3
    54. S.R. Gani, S.V. Halawar, Optimal control for the spread of infectious disease: The role of awareness programs by media and antiviral treatment, 2018, 39, 01432087, 1407, 10.1002/oca.2418
    55. Francis Maes, Raphael Fonteneau, Louis Wehenkel, Damien Ernst, 2012, Chapter 6, 978-3-642-33491-7, 37, 10.1007/978-3-642-33492-4_6
    56. Marie-José Mhawej, Cécile Brunet-François, Raphael Fonteneau, Damien Ernst, Virginie Ferré, Guy-Bart Stan, François Raffi, Claude H. Moog, Apoptosis characterizes immunological failure of HIV infected patients, 2009, 17, 09670661, 798, 10.1016/j.conengprac.2009.01.001
    57. Xia Wang, Ahmed Elaiw, Xinyu Song, Global properties of a delayed HIV infection model with CTL immune response, 2012, 218, 00963003, 9405, 10.1016/j.amc.2012.03.024
    58. Baba Seidu, Oluwole D. Makinde, Optimal Control of HIV/AIDS in the Workplace in the Presence of Careless Individuals, 2014, 2014, 1748-670X, 1, 10.1155/2014/831506
    59. Kalyan Manna, Siddhartha P. Chakrabarty, Combination therapy of pegylated interferon and lamivudine and optimal controls for chronic hepatitis B infection, 2018, 6, 2195-268X, 354, 10.1007/s40435-017-0306-x
    60. Noah F. Beggs, Hana M. Dobrovolny, Determining drug efficacy parameters for mathematical models of influenza, 2015, 9, 1751-3758, 332, 10.1080/17513758.2015.1052764
    61. Nicholas Ekow Thomford, Kevin Dzobo, Emile Chimusa, Kerstin Andrae-Marobela, Shadreck Chirikure, Ambroise Wonkam, Collet Dandara, Personalized Herbal Medicine? A Roadmap for Convergence of Herbal and Precision Medicine Biomarker Innovations, 2018, 22, 1557-8100, 375, 10.1089/omi.2018.0074
    62. Priti Kumar Roy, 2015, Chapter 1, 978-981-287-851-9, 1, 10.1007/978-981-287-852-6_1
    63. H.J. Chang, C.H. Moog, A. Astolfi, P.S. Rivadeneira, A control systems analysis of HIV prevention model using impulsive input, 2014, 13, 17468094, 123, 10.1016/j.bspc.2014.03.008
    64. Sanyi Tang, Yanni Xiao, Ning Wang, Hulin Wu, Piecewise HIV virus dynamic model with CD4+ T cell count-guided therapy: I, 2012, 308, 00225193, 123, 10.1016/j.jtbi.2012.05.022
    65. O.D. Makinde, K.O. Okosun, Impact of Chemo-therapy on Optimal Control of Malaria Disease with Infected Immigrants, 2011, 104, 03032647, 32, 10.1016/j.biosystems.2010.12.010
    66. Dana Paquin, Peter S. Kim, Peter P. Lee, Doron Levy, Strategic Treatment Interruptions During Imatinib Treatment of Chronic Myelogenous Leukemia, 2011, 73, 0092-8240, 1082, 10.1007/s11538-010-9553-0
    67. John David, Hien Tran, H. T. Banks, Receding Horizon Control of HIV, 2011, 32, 01432087, 681, 10.1002/oca.969
    68. Hyeygjeon Chang, Claude Moog, Alessandro Astolfi, Occurrence of HIV eradication for preexposure prophylaxis treatment with a deterministic HIV model, 2016, 10, 1751-8849, 237, 10.1049/iet-syb.2016.0008
    69. Hee-Dae Kwon, Jeehyun Lee, Myoungho Yoon, Feedback control of the immune response of renal transplant recipients with inequality constraints, 2016, 71, 08981221, 2338, 10.1016/j.camwa.2015.12.020
    70. Eric S. Rosenberg, Marie Davidian, H. Thomas Banks, Using mathematical modeling and control to develop structured treatment interruption strategies for HIV infection, 2007, 88, 03768716, S41, 10.1016/j.drugalcdep.2006.12.024
    71. M. J. Mhawej, C. H. Moog, F. Biafore, 2009, Chapter 310, 978-3-540-92840-9, 1263, 10.1007/978-3-540-92841-6_310
    72. Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov, Optimal Control for an SEIR Epidemic Model with Nonlinear Incidence Rate, 2018, 141, 00222526, 353, 10.1111/sapm.12227
    73. Hyuk-Jun Chang, Alessandro Astolfi, 2015, Chapter 1, 978-3-319-27655-7, 1, 10.1007/978-3-319-27656-4_1
    74. A.M. Elaiw, Global properties of a class of HIV models, 2010, 11, 14681218, 2253, 10.1016/j.nonrwa.2009.07.001
    75. H. Zarei, A. V. Kamyad, M. H. Farahi, Optimal Control of HIV Dynamic Using Embedding Method, 2011, 2011, 1748-670X, 1, 10.1155/2011/674318
    76. Xiaoming Li, Xianghui Xu, Jie Wang, Jing Li, Sheng Qin, Juxiang Yuan, Study on Prediction Model of HIV Incidence Based on GRU Neural Network Optimized by MHPSO, 2020, 8, 2169-3536, 49574, 10.1109/ACCESS.2020.2979859
    77. Damien Ernst, Guy-Bart Stan, Jorge Goncalves, Louis Wehenkel, 2006, Clinical data based optimal STI strategies for HIV: a reinforcement learning approach, 1-4244-0171-2, 667, 10.1109/CDC.2006.377527
    78. Ferrante Neri, Jari Toivanen, L. Cascella, Yew-Soon Ong, An Adaptive Multimeme Algorithm for Designing HIV Multidrug Therapies, 2009, 1545-5963, 10.1109/tcbb.2007.1039
    79. Ellina V. Grigorieva, Evgenii N. Khailov, Andrei Korobeinikov, Optimal Controls of the Highly Active Antiretroviral Therapy, 2020, 2020, 1085-3375, 1, 10.1155/2020/8107106
    80. Carlo Delfin S. Estadilla, Aurelio A. Reyes, Optimal strategies for mitigating the HIV/AIDS epidemic in the Philippines, 2020, 43, 0170-4214, 10690, 10.1002/mma.6979
    81. Hamadjam Abboubakar, Jean Claude Kamgang, Leontine Nkague Nkamba, Daniel Tieudjo, Bifurcation thresholds and optimal control in transmission dynamics of arboviral diseases, 2018, 76, 0303-6812, 379, 10.1007/s00285-017-1146-1
    82. A. M. Elaiw, A. M. Shehata, Stability and Feedback Stabilization of HIV Infection Model with Two Classes of Target Cells, 2012, 2012, 1026-0226, 1, 10.1155/2012/963864
    83. Esteban A. Hernandez-Vargas, Richard H. Middleton, Modeling the three stages in HIV infection, 2013, 320, 00225193, 33, 10.1016/j.jtbi.2012.11.028
    84. Marios M. Hadjiandreou, Raúl Conejeros, D. Ian Wilson, Planning of patient-specific drug-specific optimal HIV treatment strategies, 2009, 64, 00092509, 4024, 10.1016/j.ces.2009.06.009
    85. E.V. Grigorieva, E.N. Khailov, A. Korobeinikov, A. Morozov, S. Petrovskii, Optimal Control for a SIR Epidemic Model with Nonlinear Incidence Rate, 2016, 11, 1760-6101, 89, 10.1051/mmnp/201611407
    86. Optimal control of chikungunya disease: Larvae reduction, treatment and prevention, 2012, 9, 1551-0018, 369, 10.3934/mbe.2012.9.369
    87. Hossein Kheiri, Mohsen Jafari, Optimal control of a fractional-order model for the HIV/AIDS epidemic, 2018, 11, 1793-5245, 1850086, 10.1142/S1793524518500869
    88. Andreas Hillmann, Martin Crane, Heather J. Ruskin, HIV models for treatment interruption: Adaptation and comparison, 2017, 483, 03784371, 44, 10.1016/j.physa.2017.05.005
    89. Kazeem O. Okosun, Oluwole D. Makinde, Isaac Takaidza, Analysis of recruitment and industrial human resources management for optimal productivity in the presence of the HIV/AIDS epidemic, 2013, 39, 0092-0606, 99, 10.1007/s10867-012-9288-2
    90. Mélanie Prague, Daniel Commenges, Jon Michael Gran, Bruno Ledergerber, Jim Young, Hansjakob Furrer, Rodolphe Thiébaut, Dynamic models for estimating the effect of HAART on CD4 in observational studies: Application to the Aquitaine Cohort and the Swiss HIV Cohort Study, 2017, 73, 0006341X, 294, 10.1111/biom.12564
    91. D. M. Basavarajaiah, Bhamidipati Narasimha Murthy, 2020, Chapter 3, 978-981-15-0150-0, 87, 10.1007/978-981-15-0151-7_3
    92. Jeng-Huei Chen, An analysis of functional curability on HIV infection models with Michaelis-Menten-type immune response and its generalization, 2017, 22, 1553-524X, 2089, 10.3934/dcdsb.2017086
    93. A. Astolfi, Activation of Immune Response in Disease Dynamics via Controlled Drug Scheduling, 2009, 6, 1545-5955, 248, 10.1109/TASE.2008.2008156
    94. H. T. Banks, Hee-Dae Kwon, J. A. Toivanen, H. T. Tran, A state-dependent Riccati equation-based estimator approach for HIV feedback control, 2006, 27, 0143-2087, 93, 10.1002/oca.773
    95. P.S. Rivadeneira, C.H. Moog, Impulsive control of single-input nonlinear systems with application to HIV dynamics, 2012, 218, 00963003, 8462, 10.1016/j.amc.2012.01.071
    96. Pablo S. Rivadeneira, Claude H. Moog, Guy-Bart Stan, Cecile Brunet, François Raffi, Virginie Ferré, Vicente Costanza, Marie J. Mhawej, Federico Biafore, Djomangan A. Ouattara, Damien Ernst, Raphael Fonteneau, Xiaohua Xia, Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review, 2014, 3, 2164-7860, 233, 10.1089/biores.2014.0024
    97. Robert Smith, Kazeem Oare Okosun, Optimal control analysis of malaria–schistosomiasis co-infection dynamics, 2016, 13, 1551-0018, 2, 10.3934/mbe.2017024
    98. Ferrante Neri, Jari Toivanen, Giuseppe Leonardo Cascella, Yew-Soon Ong, An Adaptive Multimeme Algorithm for Designing HIV Multidrug Therapies, 2007, 4, 1545-5963, 264, 10.1109/TCBB.2007.070202
    99. Amar Nath Chatterjee, Priti Kumar Roy, Anti-viral drug treatment along with immune activator IL-2: a control-based mathematical approach for HIV infection, 2012, 85, 0020-7179, 220, 10.1080/00207179.2011.643414
    100. Mingwang Shen, Yanni Xiao, Libin Rong, Guihua Zhuang, Global dynamics and cost-effectiveness analysis of HIV pre-exposure prophylaxis and structured treatment interruptions based on a multi-scale model, 2019, 75, 0307904X, 162, 10.1016/j.apm.2019.05.024
    101. Seema Nanda, Helen Moore, Suzanne Lenhart, Optimal control of treatment in a mathematical model of chronic myelogenous leukemia, 2007, 210, 00255564, 143, 10.1016/j.mbs.2007.05.003
    102. Bao-Zhu Guo, Bing Sun, Dynamic programming approach to the numerical solution of optimal control with paradigm by a mathematical model for drug therapies of HIV/AIDS, 2014, 15, 1389-4420, 119, 10.1007/s11081-012-9204-4
    103. Hongyu Miao, Xiaohua Xia, Alan S. Perelson, Hulin Wu, On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics, 2011, 53, 0036-1445, 3, 10.1137/090757009
    104. Baba Seidu, Oluwole D. Makinde, Ibrahim Y. Seini, Mathematical Analysis of the Effects of HIV-Malaria Co-infection on Workplace Productivity, 2015, 63, 0001-5342, 151, 10.1007/s10441-015-9255-y
    105. N.A. Reisi, S. Hadipour Lakmesari, M.J. Mahmoodabadi, S. Hadipour, Optimum fuzzy control of human immunodeficiency virus type1 using an imperialist competitive algorithm, 2019, 16, 23529148, 100241, 10.1016/j.imu.2019.100241
    106. Qian Li, Yanni Xiao, Global Dynamics of a Virus-Immune System with Virus-Guided Therapy and Saturation Growth of Virus, 2018, 2018, 1024-123X, 1, 10.1155/2018/4710586
    107. A.M. Elaiw, X. Xia, HIV dynamics: Analysis and robust multirate MPC-based treatment schedules, 2009, 359, 0022247X, 285, 10.1016/j.jmaa.2009.05.038
    108. Aivar Sootla, Diego Oyarzún, David Angeli, Guy-Bart Stan, Shaping pulses to control bistable systems: Analysis, computation and counterexamples, 2016, 63, 00051098, 254, 10.1016/j.automatica.2015.10.037
    109. G. Dimitriu, T. Lorenzi, R. Ştefănescu, S. Anita, N. Hritonenko, G. Marinoschi, A. Swierniak, Evolutionary Dynamics of Cancer Cell Populations under Immune Selection Pressure and Optimal Control of Chemotherapy, 2014, 9, 0973-5348, 88, 10.1051/mmnp/20149406
    110. R Carrasco-Hernandez, Rodrigo Jácome, Yolanda López Vidal, Samuel Ponce de León, Are RNA Viruses Candidate Agents for the Next Global Pandemic? A Review, 2017, 58, 1084-2020, 343, 10.1093/ilar/ilx026
    111. Hee-Dae Kwon, Jeehyun Lee, Sung-Dae Yang, Optimal control of an age-structured model of HIV infection, 2012, 219, 00963003, 2766, 10.1016/j.amc.2012.09.003
    112. Jaouad Danane, Optimal control of viral infection model with saturated infection rate, 2020, 0, 2155-3297, 0, 10.3934/naco.2020031
    113. Rashid Jan, Sania Qureshi, Salah Boulaaras, Viet-Thanh Pham, Evren Hincal, Rafik Guefaifia, Optimization of the fractional-order parameter with the error analysis for human immunodeficiency virus under Caputo operator, 2023, 0, 1937-1632, 0, 10.3934/dcdss.2023010
    114. S.Y. Tchoumi, M.L. Diagne, H. Rwezaura, J.M. Tchuenche, Malaria and COVID-19 co-dynamics: A mathematical model and optimal control, 2021, 99, 0307904X, 294, 10.1016/j.apm.2021.06.016
    115. Peng Wu, Zerong He, Asaf Khan, Dynamical analysis and optimal control of an age-since infection HIV model at individuals and population levels, 2022, 106, 0307904X, 325, 10.1016/j.apm.2022.02.008
    116. A. M. Elaiw, N. H. Alshamrani, E. Dahy, A. A. Abdellatif, Stability of within host HTLV-I/HIV-1 co-infection in the presence of macrophages, 2023, 16, 1793-5245, 10.1142/S1793524522500668
    117. Aditi Mishra, Utkarsh Soni, Jinbin Huang, Chris Bryan, 2022, Why? Why not? When? Visual Explanations of Agent Behaviour in Reinforcement Learning, 978-1-6654-2335-9, 111, 10.1109/PacificVis53943.2022.00020
    118. Shabnam Ghareh Mohammadlou, Reza Shadi, Ahmad Fakharian, Nonlinear Sub-optimal Control Design for Suppressing HIV Replication, 2022, 46, 2228-6179, 805, 10.1007/s40998-022-00509-1
    119. Chao Yu, Jiming Liu, Shamim Nemati, Guosheng Yin, Reinforcement Learning in Healthcare: A Survey, 2023, 55, 0360-0300, 1, 10.1145/3477600
    120. S. KADALEKA, S. ABELMAN, P. M. MWAMTOBE, J. M. TCHUENCHE, OPTIMAL CONTROL ANALYSIS OF A HUMAN–BOVINE SCHISTOSOMIASIS MODEL, 2021, 29, 0218-3390, 1, 10.1142/S0218339021500017
    121. P M Tchepmo Djomegni, G O Olupitan, E F Dougmo Goufo, A metapopulation model for zika virus disease transmission dynamics between linked communities, 2021, 96, 0031-8949, 124049, 10.1088/1402-4896/ac2bdb
    122. A. M. Elaiw, N. H. AlShamrani, E. Dahy, A. A. Abdellatif, Aeshah A. Raezah, Effect of Macrophages and Latent Reservoirs on the Dynamics of HTLV-I and HIV-1 Coinfection, 2023, 11, 2227-7390, 592, 10.3390/math11030592
    123. Kazeem Oare Okosun, M. Mukamuri, Daniel Oluwole Makinde, Global stability analysis and control of leptospirosis, 2016, 14, 2391-5455, 567, 10.1515/math-2016-0053
    124. Elexson Nillian, Nur Diyana Zakaria, Dalene Lesen, Nur Hafizah Mohd Yusoff, Nurain Syahirah Binti Ismail, Teng Sing Tung, Lesley Bilung, Comparison Distribution of Vibrio Species in Stocking to Harvesting Process of Shrimp at Commercialize Shrimp Farm, 2022, 16, 1998-4510, 168, 10.46300/91011.2022.16.22
    125. Zhaohong Sun, Wei Dong, Haomin Li, Zhengxing Huang, Adversarial reinforcement learning for dynamic treatment regimes, 2023, 137, 15320464, 104244, 10.1016/j.jbi.2022.104244
    126. M. L. Diagne, H. Rwezaura, S. Y. Tchoumi, J. M. Tchuenche, Jan Rychtar, A Mathematical Model of COVID-19 with Vaccination and Treatment, 2021, 2021, 1748-6718, 1, 10.1155/2021/1250129
    127. Ahmed M. Elaiw, Abdulaziz K. Aljahdali, Aatef D. Hobiny, Dynamical Properties of Discrete-Time HTLV-I and HIV-1 within-Host Coinfection Model, 2023, 12, 2075-1680, 201, 10.3390/axioms12020201
    128. Ahmed M. Elaiw, Abdualaziz K. Aljahdali, Aatef D. Hobiny, Discretization and Analysis of HIV-1 and HTLV-I Coinfection Model with Latent Reservoirs, 2023, 11, 2079-3197, 54, 10.3390/computation11030054
    129. Aeshah A. Raezah, Elsayed Dahy, E. Kh. Elnahary, Shaimaa A. Azoz, Stability of HIV-1 Dynamics Models with Viral and Cellular Infections in the Presence of Macrophages, 2023, 12, 2075-1680, 617, 10.3390/axioms12070617
    130. Wisdom S. Avusuglo, Nicola Bragazzi, Ali Asgary, James Orbinski, Jianhong Wu, Jude Dzevela Kong, Leveraging an epidemic–economic mathematical model to assess human responses to COVID-19 policies and disease progression, 2023, 13, 2045-2322, 10.1038/s41598-023-39723-0
    131. Chitra A. Dhawale, Kritika Anil Dhawale, 2023, chapter 8, 9781668466469, 105, 10.4018/978-1-6684-6646-9.ch008
    132. 佳豪 张, A Model of HIV Infection with Two Types of Target Cells and Latent Infection, 2024, 13, 2324-7991, 2687, 10.12677/aam.2024.136257
    133. Yahe Yu, Hien Tran, An XGBoost-Based Fitted Q Iteration for Finding the Optimal STI Strategies for HIV Patients, 2024, 35, 2162-237X, 648, 10.1109/TNNLS.2022.3176204
    134. Taeyong Lee, Hee-Dae Kwon, Jeehyun Lee, Constrained optimal control problem of oncolytic viruses in cancer treatment, 2024, 03784754, 10.1016/j.matcom.2024.10.019
    135. Changyeon Yoon, Jaemoo Choi, Hee-Dae Kwon, Myungjoo Kang, Optimal STI controls for HIV patients based on an efficient deep Q learning method, 2024, 594, 00225193, 111914, 10.1016/j.jtbi.2024.111914
    136. Sida Kang, Xiaolin Ma, Yuhan Hu, Dynamic analysis and optimal control of competitive information dissemination model, 2024, 14, 2045-2322, 10.1038/s41598-024-82512-6
    137. Bhakti Thakre, Uma Yadav, Shweta V. Bondre, 2025, 9780443301469, 241, 10.1016/B978-0-443-30146-9.00008-3
    138. Bing Sun, Bao-Zhu Guo, Zhen-Zhen Tao, 2025, Chapter 4, 978-981-96-5738-4, 261, 10.1007/978-981-96-5739-1_4
    139. Ian Edwin Cock, Benjamin Matthews, Adriaan Erasmus Basson, Liquid Chromatography-Mass Spectrometry Metabolomic Analysis of Terminalia ferdinandiana Exell. Fruit Extracts That Inhibit HIV-1 Cell Infection, HIV-1 Reverse Transcriptase and HIV-1 Protease, 2025, 30, 1420-3049, 1701, 10.3390/molecules30081701
  • Reader Comments
  • © 2004 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(6256) PDF downloads(678) Cited by(138)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog