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Optimal controls for a 3-compartment model for cancer chemotherapy with quadratic objective
| 1. | Department of Mathematics and Statistics, UNC Wilmington, Wilmington, NC 28403, United States |
| 2. | Center for Research in Scientific Computation, Raleigh, NC 27695-8205, United States |
| 3. | Department of Math and Stat. UNCW, 601 S. College Road, Wilmington NC 28403 |
| [1] |
Shuo Wang, Heinz Schättler. Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1223-1240. doi: 10.3934/mbe.2016040 |
| [2] |
Arturo Alvarez-Arenas, Konstantin E. Starkov, Gabriel F. Calvo, Juan Belmonte-Beitia. Ultimate dynamics and optimal control of a multi-compartment model of tumor resistance to chemotherapy. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2017-2038. doi: 10.3934/dcdsb.2019082 |
| [3] |
Urszula Ledzewicz, Heinz Schättler. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 129-150. doi: 10.3934/dcdsb.2006.6.129 |
| [4] |
Urszula Ledzewicz, Heinz Schättler, Mostafa Reisi Gahrooi, Siamak Mahmoudian Dehkordi. On the MTD paradigm and optimal control for multi-drug cancer chemotherapy. Mathematical Biosciences & Engineering, 2013, 10 (3) : 803-819. doi: 10.3934/mbe.2013.10.803 |
| [5] |
Shuo Wang, Heinz Schättler. Optimal control for cancer chemotherapy under tumor heterogeneity with Michealis-Menten pharmacodynamics. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2383-2405. doi: 10.3934/dcdsb.2019100 |
| [6] |
Urszula Ledzewicz, Heinz Schättler, Shuo Wang. On the role of tumor heterogeneity for optimal cancer chemotherapy. Networks & Heterogeneous Media, 2019, 14 (1) : 131-147. doi: 10.3934/nhm.2019007 |
| [7] |
Luis A. Fernández, Cecilia Pola. Catalog of the optimal controls in cancer chemotherapy for the Gompertz model depending on PK/PD and the integral constraint. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1563-1588. doi: 10.3934/dcdsb.2014.19.1563 |
| [8] |
Urszula Ledzewicz, Heinz Schättler. Controlling a model for bone marrow dynamics in cancer chemotherapy. Mathematical Biosciences & Engineering, 2004, 1 (1) : 95-110. doi: 10.3934/mbe.2004.1.95 |
| [9] |
Urszula Ledzewicz, Heinz Schättler. The Influence of PK/PD on the Structure of Optimal Controls in Cancer Chemotherapy Models. Mathematical Biosciences & Engineering, 2005, 2 (3) : 561-578. doi: 10.3934/mbe.2005.2.561 |
| [10] |
Hsiu-Chuan Wei. Mathematical and numerical analysis of a mathematical model of mixed immunotherapy and chemotherapy of cancer. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1279-1295. doi: 10.3934/dcdsb.2016.21.1279 |
| [11] |
Craig Collins, K. Renee Fister, Bethany Key, Mary Williams. Blasting neuroblastoma using optimal control of chemotherapy. Mathematical Biosciences & Engineering, 2009, 6 (3) : 451-467. doi: 10.3934/mbe.2009.6.451 |
| [12] |
Clara Rojas, Juan Belmonte-Beitia, Víctor M. Pérez-García, Helmut Maurer. Dynamics and optimal control of chemotherapy for low grade gliomas: Insights from a mathematical model. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1895-1915. doi: 10.3934/dcdsb.2016028 |
| [13] |
Luis A. Fernández, Cecilia Pola. Optimal control problems for the Gompertz model under the Norton-Simon hypothesis in chemotherapy. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2577-2612. doi: 10.3934/dcdsb.2018266 |
| [14] |
Urszula Ledzewicz, Behrooz Amini, Heinz Schättler. Dynamics and control of a mathematical model for metronomic chemotherapy. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1257-1275. doi: 10.3934/mbe.2015.12.1257 |
| [15] |
Heinz Schättler, Urszula Ledzewicz. Fields of extremals and sensitivity analysis for multi-input bilinear optimal control problems. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4611-4638. doi: 10.3934/dcds.2015.35.4611 |
| [16] |
Urszula Ledzewicz, Shuo Wang, Heinz Schättler, Nicolas André, Marie Amélie Heng, Eddy Pasquier. On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach. Mathematical Biosciences & Engineering, 2017, 14 (1) : 217-235. doi: 10.3934/mbe.2017014 |
| [17] |
Joseph Malinzi, Rachid Ouifki, Amina Eladdadi, Delfim F. M. Torres, K. A. Jane White. Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1435-1463. doi: 10.3934/mbe.2018066 |
| [18] |
Alexis B. Cook, Daniel R. Ziazadeh, Jianfeng Lu, Trachette L. Jackson. An integrated cellular and sub-cellular model of cancer chemotherapy and therapies that target cell survival. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1219-1235. doi: 10.3934/mbe.2015.12.1219 |
| [19] |
María Barbero-Liñán, Miguel C. Muñoz-Lecanda. Strict abnormal extremals in nonholonomic and kinematic control systems. Discrete & Continuous Dynamical Systems - S, 2010, 3 (1) : 1-17. doi: 10.3934/dcdss.2010.3.1 |
| [20] |
Ben Sheller, Domenico D'Alessandro. Analysis of a cancer dormancy model and control of immuno-therapy. Mathematical Biosciences & Engineering, 2015, 12 (5) : 1037-1053. doi: 10.3934/mbe.2015.12.1037 |
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