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Optimal control of effector-tumor-normal cells dynamics in presence of adoptive immunotherapy. (English) Zbl 1525.92027

MSC:

92C50 Medical applications (general)
34C60 Qualitative investigation and simulation of ordinary differential equation models
34H05 Control problems involving ordinary differential equations
49K15 Optimality conditions for problems involving ordinary differential equations
49N90 Applications of optimal control and differential games
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[1] L, The dynamics of an optimally controlled tumor model: A case study, Math. Comput. Model., 37, 1221-1244 (2003) · Zbl 1043.92018 · doi:10.1016/S0895-7177(03)00133-X
[2] A, The chaos and optimal control of cancer model with complete unknown parameters, Chaos Soliton. Fract., 42, 2865-2874 (2009) · Zbl 1198.37044 · doi:10.1016/j.chaos.2009.04.028
[3] A, Cellular and Molecular Immunology E-Book, Elsevier Health Sciences (2011)
[4] G. Prendergast, E. Jaffee, <i>Cancer immunotherapy: Immune suppression and tumor growth</i>, Academic Press, 2013.
[5] M, An extended mathematical model of tumor growth and its interaction with the immune system, to be used for developing an optimized immunotherapy treatment protocol, Math. Biosci., 292, 1-9 (2017) · Zbl 1376.92026 · doi:10.1016/j.mbs.2017.07.006
[6] S, The combined effects of optimal control in cancer remission, Appl. Math. Comput., 271, 375-388 (2015) · Zbl 1410.92048
[7] V, Modeling tumor regrowth and immunotherapy, Math. Comput. Model., 33, 1275-1287 (2001) · Zbl 1004.92021 · doi:10.1016/S0895-7177(00)00314-9
[8] D, Mathematical prostate cancer evolution: Effect of immunotherapy based on controlled vaccination, Comput. Math. Method. M., 2020, 1-8 (2020) · Zbl 1431.92050
[9] T, Optimal control applied to immunotherapy, Discrete Cont. Dyn. B, 4, 135-146 (2004) · Zbl 1042.92013
[10] F, A dynamical model of tumour immunotherapy, Math. Biosci., 253, 50-62 (2014) · Zbl 1287.92008 · doi:10.1016/j.mbs.2014.04.003
[11] L, Mathematical modelling and analysis of the tumor treatment regimens with pulsed immunotherapy and chemotherapy, Comput. Math. Method. M., 2016, 1-12 (2016) · Zbl 1348.92085
[12] M, A recommendation to oncologists for cancer treatment by immunotherapy: Quantitative and qualitative analysis, International Journal of Biomedical and Biological Engineering, 13, 1-6 (2019)
[13] N, Adoptive cellular immunotherapy for solid tumors, Int. J. Tumor Ther., 9, 1-4 (2020)
[14] W, The stability analysis of tumor-immune responses to chemotherapy system with gaussian white noises, Chaos Soliton. Fract., 127, 96-102 (2019) · doi:10.1016/j.chaos.2019.06.030
[15] M, The impact of distributed time delay in a tumor-immune interaction system, Chaos Soliton. Fract., 142, 110483 (2021) · Zbl 1496.92021 · doi:10.1016/j.chaos.2020.110483
[16] V, Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis, B. Math. Biol., 56, 295-321 (1994) · Zbl 0789.92019 · doi:10.1016/S0092-8240(05)80260-5
[17] L, A validated mathematical model of a cell-mediated immune response to tumor growth, Cancer Res., 65, 7950-7958 (2005) · doi:10.1158/0008-5472.CAN-05-0564
[18] M, Dynamical behavior of combinational immune boost against tumor, Jpn. J. Ind. App. Math., 32, 759-770 (2015) · Zbl 1339.92033 · doi:10.1007/s13160-015-0193-5
[19] U, Antiangiogenic therapy in cancer treatment as an optimal control problem, SIAM J. Control Optim., 46, 1052-1079 (2007) · Zbl 1357.49086 · doi:10.1137/060665294
[20] A, Chaos and optimal control of cancer self-remission and tumor system steady states, Chaos Soliton. Fract., 37, 1305-1316 (2008) · Zbl 1142.92327 · doi:10.1016/j.chaos.2006.10.060
[21] S, Dynamical behaviour of a tumor-immune system with chemotherapy and optimal control, J. Nonlinear Dyn., 2013, 1-13 (2013) · Zbl 1407.92066
[22] N, Analysis and optimal control in the cancer treatment model by combining radio and anti-angiogenic therapy, IJCSAM, 3, 55-60 (2017) · doi:10.12962/j24775401.v3i2.2288
[23] A, An optimal control approach for the treatment of solid tumors with angiogenesis inhibitors, Mathematics, 5, 1-14 (2017) · Zbl 1394.92057
[24] A, Optimal control analysis of combined chemotherapy-immunotherapy treatment regimens in a PKPD cancer evolution model, Biomath., 9, 1-12 (2020) · Zbl 1505.92094
[25] J, Mathematical modelling of the dynamics of tumor growth and its optimal control, International Journal of Ground Sediment & Water, 11, 659-679 (2020)
[26] I, Cancer immunoediting: A process driven by metabolic competition as a predator-prey-shared resource type model, J. Theor. Biol., 380, 463-472 (2015) · Zbl 1343.92228 · doi:10.1016/j.jtbi.2015.06.007
[27] J, Developing a minimally structured mathematical model of cancer treatment with oncolytic viruses and dendritic cell injections, Comput. Math. Method. M., 2018, 1-14 (2018) · Zbl 1431.92053
[28] P, Mathematical modeling, analysis, and simulation of tumor dynamics with drug interventions, Comput. Math. Method. M., 2019, 4079298 (2019) · Zbl 1428.92055
[29] W, The unified colored noise approximation of multidimensional stochastic dynamic system, Physica A, 555, 124624 (2020) · Zbl 1496.60080 · doi:10.1016/j.physa.2020.124624
[30] J, Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis, Math. Biosci. Eng., 15, 1435-1463 (2018) · Zbl 1416.92091 · doi:10.3934/mbe.2018066
[31] D. L. Lukes, <i>Differential equations, Classical to controlled</i>, Academic Press, 1982. · Zbl 0509.34003
[32] W. H. Fleming, R. W. Rishel, <i>Deterministic and stochastic optimal control</i>, Springer, 1975. · Zbl 0323.49001
[33] L, The mathematical theory of optimal process, Gordon and Breach (1962)
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