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A spatial model of tumor-host interaction: Application of chemotherapy
1. | Institute for Mathematics and its Applications, University of Minnesota, 114 Lind Hall, Minneapolis, MN 55455, United States |
2. | Niels Bohr Institute, Center for Models of Life, Blegdamsvej 17, 2100 Copenhagen, Denmark |
3. | Department of Cancer Biology, Vanderbilt University, Nashville, TN 37232, United States, United States |
4. | Department of Chemistry, Vanderbilt University, Nashville, TN 37235, United States |
5. | Department of Surgical Research, Beckman Research Institute of City of Hope, Duarte, CA 91010, United States |
6. | Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States, United States |
7. | Department of Applied Mathematics and Department of Pathology, University of Washington, Seattle, WA 98195, United States, United States |
8. | Department of Biomedical Engineering, Vanderbilt University, Nashville, TN 37232, United States |
9. | H. Lee Moffitt Cancer Center & Research Institute, Integrated Mathematical Oncology, 12902 Magnolia Drive, Tampa, FL 33612, United States |
[1] |
Manuel Delgado, Cristian Morales-Rodrigo, Antonio Suárez. Anti-angiogenic therapy based on the binding to receptors. Discrete and Continuous Dynamical Systems, 2012, 32 (11) : 3871-3894. doi: 10.3934/dcds.2012.32.3871 |
[2] |
Filippo Cacace, Valerio Cusimano, Alfredo Germani, Pasquale Palumbo, Federico Papa. Closed-loop control of tumor growth by means of anti-angiogenic administration. Mathematical Biosciences & Engineering, 2018, 15 (4) : 827-839. doi: 10.3934/mbe.2018037 |
[3] |
Maciej Leszczyński, Urszula Ledzewicz, Heinz Schättler. Optimal control for a mathematical model for anti-angiogenic treatment with Michaelis-Menten pharmacodynamics. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2315-2334. doi: 10.3934/dcdsb.2019097 |
[4] |
Cristian Morales-Rodrigo. A therapy inactivating the tumor angiogenic factors. Mathematical Biosciences & Engineering, 2013, 10 (1) : 185-198. doi: 10.3934/mbe.2013.10.185 |
[5] |
Urszula Ledzewicz, Helmut Maurer, Heinz Schättler. Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy. Mathematical Biosciences & Engineering, 2011, 8 (2) : 307-323. doi: 10.3934/mbe.2011.8.307 |
[6] |
Adam Glick, Antonio Mastroberardino. Combined therapy for treating solid tumors with chemotherapy and angiogenic inhibitors. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5281-5304. doi: 10.3934/dcdsb.2020343 |
[7] |
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 |
[8] |
Baba Issa Camara, Houda Mokrani, Evans K. Afenya. Mathematical modeling of glioma therapy using oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 565-578. doi: 10.3934/mbe.2013.10.565 |
[9] |
Sophia R-J Jang, Hsiu-Chuan Wei. On a mathematical model of tumor-immune system interactions with an oncolytic virus therapy. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 3261-3295. doi: 10.3934/dcdsb.2021184 |
[10] |
Urszula Ledzewicz, Heinz Schättler. On the optimality of singular controls for a class of mathematical models for tumor anti-angiogenesis. Discrete and Continuous Dynamical Systems - B, 2009, 11 (3) : 691-715. doi: 10.3934/dcdsb.2009.11.691 |
[11] |
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 |
[12] |
Heinz Schättler, Urszula Ledzewicz, Benjamin Cardwell. Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis. Mathematical Biosciences & Engineering, 2011, 8 (2) : 355-369. doi: 10.3934/mbe.2011.8.355 |
[13] |
Reihaneh Mostolizadeh, Zahra Afsharnezhad, Anna Marciniak-Czochra. Mathematical model of Chimeric Anti-gene Receptor (CAR) T cell therapy with presence of cytokine. Numerical Algebra, Control and Optimization, 2018, 8 (1) : 63-80. doi: 10.3934/naco.2018004 |
[14] |
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 |
[15] |
Urszula Ledzewicz, Mozhdeh Sadat Faraji Mosalman, Heinz Schättler. Optimal controls for a mathematical model of tumor-immune interactions under targeted chemotherapy with immune boost. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 1031-1051. doi: 10.3934/dcdsb.2013.18.1031 |
[16] |
Yueping Dong, Rinko Miyazaki, Yasuhiro Takeuchi. Mathematical modeling on helper T cells in a tumor immune system. Discrete and Continuous Dynamical Systems - B, 2014, 19 (1) : 55-72. doi: 10.3934/dcdsb.2014.19.55 |
[17] |
Sandesh Athni Hiremath, Christina Surulescu, Anna Zhigun, Stefanie Sonner. On a coupled SDE-PDE system modeling acid-mediated tumor invasion. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2339-2369. doi: 10.3934/dcdsb.2018071 |
[18] |
Niklas Kolbe, Nikolaos Sfakianakis, Christian Stinner, Christina Surulescu, Jonas Lenz. Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence. Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : 443-481. doi: 10.3934/dcdsb.2020284 |
[19] |
Kentarou Fujie, Akio Ito, Michael Winkler, Tomomi Yokota. Stabilization in a chemotaxis model for tumor invasion. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 151-169. doi: 10.3934/dcds.2016.36.151 |
[20] |
Ismail Abdulrashid, Xiaoying Han. A mathematical model of chemotherapy with variable infusion. Communications on Pure and Applied Analysis, 2020, 19 (4) : 1875-1890. doi: 10.3934/cpaa.2020082 |
2018 Impact Factor: 1.313
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