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Immunotherapy: An Optimal Control Theory Approach
Critical-Point Analysis For Three-Variable Cancer Angiogenesis Models
1. | Institute of Applied Mathematics, Informatics and Mechanics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland |
2. | Institute for Medical BioMathematics, 10 Hate'ena St., POB 282, Bene Ataroth, Israel, Israel |
[1] |
V. Lanza, D. Ambrosi, L. Preziosi. Exogenous control of vascular network formation in vitro: a mathematical model. Networks and Heterogeneous Media, 2006, 1 (4) : 621-637. doi: 10.3934/nhm.2006.1.621 |
[2] |
Zejia Wang, Haihua Zhou, Huijuan Song. The impact of time delay and angiogenesis in a tumor model. Discrete and Continuous Dynamical Systems - B, 2022, 27 (7) : 4097-4119. doi: 10.3934/dcdsb.2021219 |
[3] |
Yaodan Huang, Zhengce Zhang, Bei Hu. Bifurcation from stability to instability for a free boundary tumor model with angiogenesis. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 2473-2510. doi: 10.3934/dcds.2019105 |
[4] |
Telma Silva, Adélia Sequeira, Rafael F. Santos, Jorge Tiago. Existence, uniqueness, stability and asymptotic behavior of solutions for a mathematical model of atherosclerosis. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 343-362. doi: 10.3934/dcdss.2016.9.343 |
[5] |
Marek Bodnar, Monika Joanna Piotrowska, Urszula Foryś, Ewa Nizińska. Model of tumour angiogenesis -- analysis of stability with respect to delays. Mathematical Biosciences & Engineering, 2013, 10 (1) : 19-35. doi: 10.3934/mbe.2013.10.19 |
[6] |
Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367 |
[7] |
Keng Deng, Yixiang Wu. Asymptotic behavior for a reaction-diffusion population model with delay. Discrete and Continuous Dynamical Systems - B, 2015, 20 (2) : 385-395. doi: 10.3934/dcdsb.2015.20.385 |
[8] |
Xiaoming Zheng, Gou Young Koh, Trachette Jackson. A continuous model of angiogenesis: Initiation, extension, and maturation of new blood vessels modulated by vascular endothelial growth factor, angiopoietins, platelet-derived growth factor-B, and pericytes. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 1109-1154. doi: 10.3934/dcdsb.2013.18.1109 |
[9] |
Ling Zhang, Xiaoqi Sun. Stability analysis of time-varying delay neural network for convex quadratic programming with equality constraints and inequality constraints. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022035 |
[10] |
Zhipeng Qiu, Jun Yu, Yun Zou. The asymptotic behavior of a chemostat model. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 721-727. doi: 10.3934/dcdsb.2004.4.721 |
[11] |
Zvia Agur, L. Arakelyan, P. Daugulis, Y. Ginosar. Hopf point analysis for angiogenesis models. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 29-38. doi: 10.3934/dcdsb.2004.4.29 |
[12] |
Zhao-Xing Yang, Guo-Bao Zhang, Ge Tian, Zhaosheng Feng. Stability of non-monotone non-critical traveling waves in discrete reaction-diffusion equations with time delay. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 581-603. doi: 10.3934/dcdss.2017029 |
[13] |
Jacopo De Simoi. Stability and instability results in a model of Fermi acceleration. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 719-750. doi: 10.3934/dcds.2009.25.719 |
[14] |
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 |
[15] |
Hunseok Kang. Asymptotic behavior of a discrete turing model. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 265-284. doi: 10.3934/dcds.2010.27.265 |
[16] |
Zhi-An Wang. Wavefront of an angiogenesis model. Discrete and Continuous Dynamical Systems - B, 2012, 17 (8) : 2849-2860. doi: 10.3934/dcdsb.2012.17.2849 |
[17] |
Yuncherl Choi, Taeyoung Ha, Jongmin Han, Sewoong Kim, Doo Seok Lee. Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4255-4281. doi: 10.3934/dcds.2021035 |
[18] |
Mostafa Adimy, Fabien Crauste. Modeling and asymptotic stability of a growth factor-dependent stem cell dynamics model with distributed delay. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 19-38. doi: 10.3934/dcdsb.2007.8.19 |
[19] |
Meng Liu, Chuanzhi Bai, Yi Jin. Population dynamical behavior of a two-predator one-prey stochastic model with time delay. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2513-2538. doi: 10.3934/dcds.2017108 |
[20] |
Chaoying Li, Xiaojing Xu, Zhuan Ye. On long-time asymptotic behavior for solutions to 2D temperature-dependent tropical climate model. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1535-1568. doi: 10.3934/dcds.2021163 |
2018 Impact Factor: 1.313
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