-
Previous Article
A hierarchy of cancer models and their mathematical challenges
- DCDS-B Home
- This Issue
-
Next Article
The steady state of a maturity structured tumor cord cell population
Optimal control applied to immunotherapy
1. | Department of Mathematics, University of Kentucky, Lexington, KY 40504, United States |
2. | Department of Mathematics and Statistics, Murray State University, 6C Faculty Hall, Murray, KY 42071, United States, United States |
[1] |
K. Renee Fister, Jennifer Hughes Donnelly. Immunotherapy: An Optimal Control Theory Approach. Mathematical Biosciences & Engineering, 2005, 2 (3) : 499-510. doi: 10.3934/mbe.2005.2.499 |
[2] |
Urszula Ledzewicz, Heinz Schättler. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete and Continuous Dynamical Systems - B, 2006, 6 (1) : 129-150. doi: 10.3934/dcdsb.2006.6.129 |
[3] |
Hsiu-Chuan Wei. Mathematical and numerical analysis of a mathematical model of mixed immunotherapy and chemotherapy of cancer. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1279-1295. doi: 10.3934/dcdsb.2016.21.1279 |
[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 of a mathematical model for cancer chemotherapy under tumor heterogeneity. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1223-1240. doi: 10.3934/mbe.2016040 |
[6] |
K. E. Starkov, Svetlana Bunimovich-Mendrazitsky. Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy. Mathematical Biosciences & Engineering, 2016, 13 (5) : 1059-1075. doi: 10.3934/mbe.2016030 |
[7] |
Shuo Wang, Heinz Schättler. Optimal control for cancer chemotherapy under tumor heterogeneity with Michealis-Menten pharmacodynamics. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2383-2405. doi: 10.3934/dcdsb.2019100 |
[8] |
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 |
[9] |
Nasser Sweilam, Fathalla Rihan, Seham AL-Mekhlafi. A fractional-order delay differential model with optimal control for cancer treatment based on synergy between anti-angiogenic and immune cell therapies. Discrete and Continuous Dynamical Systems - S, 2020, 13 (9) : 2403-2424. doi: 10.3934/dcdss.2020120 |
[10] |
Amina Eladdadi, Noura Yousfi, Abdessamad Tridane. Preface: Special issue on cancer modeling, analysis and control. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : i-iii. doi: 10.3934/dcdsb.2013.18.4i |
[11] |
Urszula Ledzewicz, Heinz Schättler, Shuo Wang. On the role of tumor heterogeneity for optimal cancer chemotherapy. Networks and Heterogeneous Media, 2019, 14 (1) : 131-147. doi: 10.3934/nhm.2019007 |
[12] |
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 |
[13] |
Benedetto Piccoli. Optimal syntheses for state constrained problems with application to optimization of cancer therapies. Mathematical Control and Related Fields, 2012, 2 (4) : 383-398. doi: 10.3934/mcrf.2012.2.383 |
[14] |
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 |
[15] |
Wei Feng, Shuhua Hu, Xin Lu. Optimal controls for a 3-compartment model for cancer chemotherapy with quadratic objective. Conference Publications, 2003, 2003 (Special) : 544-553. doi: 10.3934/proc.2003.2003.544 |
[16] |
Ellina Grigorieva, Evgenii Khailov. Optimal control of pollution stock. Conference Publications, 2011, 2011 (Special) : 578-588. doi: 10.3934/proc.2011.2011.578 |
[17] |
Hang-Chin Lai, Jin-Chirng Lee, Shuh-Jye Chern. A variational problem and optimal control. Journal of Industrial and Management Optimization, 2011, 7 (4) : 967-975. doi: 10.3934/jimo.2011.7.967 |
[18] |
Denise E. Kirschner, Alexei Tsygvintsev. On the global dynamics of a model for tumor immunotherapy. Mathematical Biosciences & Engineering, 2009, 6 (3) : 573-583. doi: 10.3934/mbe.2009.6.573 |
[19] |
Frédérique Billy, Jean Clairambault. Designing proliferating cell population models with functional targets for control by anti-cancer drugs. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 865-889. doi: 10.3934/dcdsb.2013.18.865 |
[20] |
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 and Continuous Dynamical Systems - B, 2014, 19 (6) : 1563-1588. doi: 10.3934/dcdsb.2014.19.1563 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]