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The dynamics of tumor growth and cells pattern morphology
Finite-difference and pseudo-spectral methods for the numerical simulations of in vitro human tumor cell population kinetics
1. | Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287, United States |
2. | Department of Mathematics, Boise State University, 1910 University Drive, Boise, Idaho 83725, United States |
3. | Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, New Zealand |
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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 |
[2] |
Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel. On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells. Mathematical Biosciences & Engineering, 2015, 12 (1) : 163-183. doi: 10.3934/mbe.2015.12.163 |
[3] |
Evans K. Afenya, Calixto P. Calderón. Growth kinetics of cancer cells prior to detection and treatment: An alternative view. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 25-28. doi: 10.3934/dcdsb.2004.4.25 |
[4] |
Elena Izquierdo-Kulich, Margarita Amigó de Quesada, Carlos Manuel Pérez-Amor, Magda Lopes Texeira, José Manuel Nieto-Villar. The dynamics of tumor growth and cells pattern morphology. Mathematical Biosciences & Engineering, 2009, 6 (3) : 547-559. doi: 10.3934/mbe.2009.6.547 |
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Najat Ziyadi. A male-female mathematical model of human papillomavirus (HPV) in African American population. Mathematical Biosciences & Engineering, 2017, 14 (1) : 339-358. doi: 10.3934/mbe.2017022 |
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Tzy-Wei Hwang, Feng-Bin Wang. Dynamics of a dengue fever transmission model with crowding effect in human population and spatial variation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (1) : 147-161. doi: 10.3934/dcdsb.2013.18.147 |
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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 |
[8] |
Chengjun Guo, Chengxian Guo, Sameed Ahmed, Xinfeng Liu. Moment stability for nonlinear stochastic growth kinetics of breast cancer stem cells with time-delays. Discrete and Continuous Dynamical Systems - B, 2016, 21 (8) : 2473-2489. doi: 10.3934/dcdsb.2016056 |
[9] |
Frédérique Billy, Jean Clairambault, Franck Delaunay, Céline Feillet, Natalia Robert. Age-structured cell population model to study the influence of growth factors on cell cycle dynamics. Mathematical Biosciences & Engineering, 2013, 10 (1) : 1-17. doi: 10.3934/mbe.2013.10.1 |
[10] |
Jiying Ma, Dongmei Xiao. Nonlinear dynamics of a mathematical model on action potential duration and calcium transient in paced cardiac cells. Discrete and Continuous Dynamical Systems - B, 2013, 18 (9) : 2377-2396. doi: 10.3934/dcdsb.2013.18.2377 |
[11] |
Marcello Delitala, Tommaso Lorenzi. Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Mathematical Biosciences & Engineering, 2017, 14 (1) : 79-93. doi: 10.3934/mbe.2017006 |
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Renato Soeiro, Abdelrahim Mousa, Tânia R. Oliveira, Alberto A. Pinto. Dynamics of human decisions. Journal of Dynamics and Games, 2014, 1 (1) : 121-151. doi: 10.3934/jdg.2014.1.121 |
[13] |
A. K. Misra, Gauri Agrawal, Kusum Lata. Modeling the influence of human population and human population augmented pollution on rainfall. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 2979-3003. doi: 10.3934/dcdsb.2021169 |
[14] |
Yu-Hsien Chang, Guo-Chin Jau. The behavior of the solution for a mathematical model for analysis of the cell cycle. Communications on Pure and Applied Analysis, 2006, 5 (4) : 779-792. doi: 10.3934/cpaa.2006.5.779 |
[15] |
Robert P. Gilbert, Philippe Guyenne, Ying Liu. Modeling of the kinetics of vitamin D$_3$ in osteoblastic cells. Mathematical Biosciences & Engineering, 2013, 10 (2) : 319-344. doi: 10.3934/mbe.2013.10.319 |
[16] |
Diego Samuel Rodrigues, Paulo Fernando de Arruda Mancera. Mathematical analysis and simulations involving chemotherapy and surgery on large human tumours under a suitable cell-kill functional response. Mathematical Biosciences & Engineering, 2013, 10 (1) : 221-234. doi: 10.3934/mbe.2013.10.221 |
[17] |
D. Criaco, M. Dolfin, L. Restuccia. Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 59-73. doi: 10.3934/mbe.2013.10.59 |
[18] |
Alan D. Rendall. Multiple steady states in a mathematical model for interactions between T cells and macrophages. Discrete and Continuous Dynamical Systems - B, 2013, 18 (3) : 769-782. doi: 10.3934/dcdsb.2013.18.769 |
[19] |
Avner Friedman, Yangjin Kim. Tumor cells proliferation and migration under the influence of their microenvironment. Mathematical Biosciences & Engineering, 2011, 8 (2) : 371-383. doi: 10.3934/mbe.2011.8.371 |
[20] |
Meng Liu, Yuxiang Li. Global generalized solutions of a haptotaxis model describing cancer cells invasion and metastatic spread. Communications on Pure and Applied Analysis, 2022, 21 (3) : 927-942. doi: 10.3934/cpaa.2022004 |
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