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Modelling cell populations with spatial structure: Steady state and treatment-induced evolution
A mathematical model of prostate tumor growth and androgen-independent relapse
1. | Department of Mathematics, University of Michigan, Ann Arbor, Michigan |
[1] |
Avner Friedman, Harsh Vardhan Jain. A partial differential equation model of metastasized prostatic cancer. Mathematical Biosciences & Engineering, 2013, 10 (3) : 591-608. doi: 10.3934/mbe.2013.10.591 |
[2] |
Alacia M. Voth, John G. Alford, Edward W. Swim. Mathematical modeling of continuous and intermittent androgen suppression for the treatment of advanced prostate cancer. Mathematical Biosciences & Engineering, 2017, 14 (3) : 777-804. doi: 10.3934/mbe.2017043 |
[3] |
Erica M. Rutter, Yang Kuang. Global dynamics of a model of joint hormone treatment with dendritic cell vaccine for prostate cancer. Discrete and Continuous Dynamical Systems - B, 2017, 22 (3) : 1001-1021. doi: 10.3934/dcdsb.2017050 |
[4] |
Tania Biswas, Elisabetta Rocca. Long time dynamics of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2455-2469. doi: 10.3934/dcdsb.2021140 |
[5] |
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 |
[6] |
J. Ignacio Tello. On a mathematical model of tumor growth based on cancer stem cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 263-278. doi: 10.3934/mbe.2013.10.263 |
[7] |
Marcello Delitala, Tommaso Lorenzi. Recognition and learning in a mathematical model for immune response against cancer. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 891-914. doi: 10.3934/dcdsb.2013.18.891 |
[8] |
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 |
[9] |
Harsh Vardhan Jain, Avner Friedman. Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 945-967. doi: 10.3934/dcdsb.2013.18.945 |
[10] |
Ebraheem O. Alzahrani, Muhammad Altaf Khan. Androgen driven evolutionary population dynamics in prostate cancer growth. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3419-3440. doi: 10.3934/dcdss.2020426 |
[11] |
Frederic Abergel, Remi Tachet. A nonlinear partial integro-differential equation from mathematical finance. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 907-917. doi: 10.3934/dcds.2010.27.907 |
[12] |
Herbert Koch. Partial differential equations with non-Euclidean geometries. Discrete and Continuous Dynamical Systems - S, 2008, 1 (3) : 481-504. doi: 10.3934/dcdss.2008.1.481 |
[13] |
Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 471-487. doi: 10.3934/dcds.2020264 |
[14] |
Wilhelm Schlag. Spectral theory and nonlinear partial differential equations: A survey. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 703-723. doi: 10.3934/dcds.2006.15.703 |
[15] |
Eugenia N. Petropoulou, Panayiotis D. Siafarikas. Polynomial solutions of linear partial differential equations. Communications on Pure and Applied Analysis, 2009, 8 (3) : 1053-1065. doi: 10.3934/cpaa.2009.8.1053 |
[16] |
Arnulf Jentzen. Taylor expansions of solutions of stochastic partial differential equations. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 515-557. doi: 10.3934/dcdsb.2010.14.515 |
[17] |
Barbara Abraham-Shrauner. Exact solutions of nonlinear partial differential equations. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 577-582. doi: 10.3934/dcdss.2018032 |
[18] |
Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete and Continuous Dynamical Systems - B, 2017, 22 (8) : 3127-3144. doi: 10.3934/dcdsb.2017167 |
[19] |
Runzhang Xu. Preface: Special issue on advances in partial differential equations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : i-i. doi: 10.3934/dcdss.2021137 |
[20] |
Avner Friedman. A hierarchy of cancer models and their mathematical challenges. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 147-159. doi: 10.3934/dcdsb.2004.4.147 |
2020 Impact Factor: 1.327
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