This paper is devoted to a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to the tumor angiogenic factors. The main feature of the model under consideration is a nonlinear flux production of tumor angiogenic factors at the boundary of the tumor. It is proved the global existence for the nonlinear system and the effect in the large time behavior of the system for high doses of the therapeutic agent.
Citation: Cristian Morales-Rodrigo. A therapy inactivating the tumor angiogenic factors[J]. Mathematical Biosciences and Engineering, 2013, 10(1): 185-198. doi: 10.3934/mbe.2013.10.185
Related Papers:
| [1] |
Urszula Ledzewicz, Helmut Maurer, Heinz Schättler .
Optimal and suboptimal protocols for a mathematical model for
tumor anti-angiogenesis in combination with chemotherapy. Mathematical Biosciences and Engineering, 2011, 8(2): 307-323.
doi: 10.3934/mbe.2011.8.307
|
| [2] |
Urszula Foryś, Yuri Kheifetz, Yuri Kogan .
Critical-Point Analysis For Three-Variable Cancer Angiogenesis Models. Mathematical Biosciences and Engineering, 2005, 2(3): 511-525.
doi: 10.3934/mbe.2005.2.511
|
| [3] |
John D. Nagy, Dieter Armbruster .
Evolution of uncontrolled proliferation and the angiogenic switch in cancer. Mathematical Biosciences and Engineering, 2012, 9(4): 843-876.
doi: 10.3934/mbe.2012.9.843
|
| [4] |
Filippo Cacace, Valerio Cusimano, Alfredo Germani, Pasquale Palumbo, Federico Papa .
Closed-loop control of tumor growth by means of anti-angiogenic administration. Mathematical Biosciences and Engineering, 2018, 15(4): 827-839.
doi: 10.3934/mbe.2018037
|
| [5] |
Jerzy Klamka, Helmut Maurer, Andrzej Swierniak .
Local controllability and optimal control for\newline a model of combined anticancer therapy with control delays. Mathematical Biosciences and Engineering, 2017, 14(1): 195-216.
doi: 10.3934/mbe.2017013
|
| [6] |
Mahya Mohammadi, M. Soltani, Cyrus Aghanajafi, Mohammad Kohandel .
Investigation of the evolution of tumor-induced microvascular network under the inhibitory effect of anti-angiogenic factor, angiostatin: A mathematical study. Mathematical Biosciences and Engineering, 2023, 20(3): 5448-5480.
doi: 10.3934/mbe.2023252
|
| [7] |
Donggu Lee, Sunju Oh, Sean Lawler, Yangjin Kim .
Bistable dynamics of TAN-NK cells in tumor growth and control of radiotherapy-induced neutropenia in lung cancer treatment. Mathematical Biosciences and Engineering, 2025, 22(4): 744-809.
doi: 10.3934/mbe.2025028
|
| [8] |
Dehua Feng, Xi Chen, Xiaoyu Wang, Xuanqin Mou, Ling Bai, Shu Zhang, Zhiguo Zhou .
Predicting effectiveness of anti-VEGF injection through self-supervised learning in OCT images. Mathematical Biosciences and Engineering, 2023, 20(2): 2439-2458.
doi: 10.3934/mbe.2023114
|
| [9] |
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 and Engineering, 2015, 12(6): 1219-1235.
doi: 10.3934/mbe.2015.12.1219
|
| [10] |
Rujing Zhao, Xiulan Lai .
Evolutionary analysis of replicator dynamics about anti-cancer combination therapy. Mathematical Biosciences and Engineering, 2023, 20(1): 656-682.
doi: 10.3934/mbe.2023030
|
Abstract
This paper is devoted to a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to the tumor angiogenic factors. The main feature of the model under consideration is a nonlinear flux production of tumor angiogenic factors at the boundary of the tumor. It is proved the global existence for the nonlinear system and the effect in the large time behavior of the system for high doses of the therapeutic agent.
References
|
[1]
|
in "Function Spaces, Differential Operators and Nonlinear Analysis" (editors, H. J. Schmeisser and H. Triebel), Teubner, Stuttgart, Leipzig, (1993), 9-126.
|
|
[2]
|
J. Differential Equations, 146 (1998), 336-374.
|
|
[3]
|
Bull. Math. Biol., 60 (1998), 857-899.
|
|
[4]
|
IMA J. Math. Appl. Med. Biol., 10 (1993), 149-168.
|
|
[5]
|
Math. Comput. Modelling, 23 (1996), 47-87.
|
|
[6]
|
Preprint, arXiv:1202.4695.
|
|
[7]
|
Nonlinear Anal., 72 (2010), 330-347.
|
|
[8]
|
Discrete Contin. Dyn. Syst. Ser A, 32 (2012), 3871-3894.
|
|
[9]
|
Nonlinear Analysis RWA, 11 (2010), 3884-3902.
|
|
[10]
|
J. Differential Equations, 244 (2008), 3119-3150.
|
|
[11]
|
SIAM J. Math. Anal., 33 (2002), 1330-1350.
|
|
[12]
|
Comm. Comtemporary Math., 11 (2009), 585-613.
|
|
[13]
|
Lecture Notes Math., 840, Springer 1981.
|
|
[14]
|
J. Math. Biol., 42 (2001), 195-238.
|
|
[15]
|
ESAIM Math. Modelling Num. Anal., 37 (2003), 581-599.
|
|
[16]
|
J. Math. Biol., 49 (2004), 111-187.
|
|
[17]
|
J. Math. Biol., 58 (2009), 689-721.
|
|
[18]
|
Science, 240 (1988), 177-184.
|
|
[19]
|
J. Differential Equations, 248 (2010), 2889-2905.
|
DownLoad: