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Inside mathematical modeling: building models in the context of wound healing in bone
Growth kinetics of cancer cells prior to detection and treatment: An alternative view
| 1. | Department of Mathematics, Elmhurst College, 190 Prospect Avenue, Elmhurst, IL 60126, United States |
| 2. | Department of Mathematics, Statistics, and Computer Science (MC 249), University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, United States |
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Urszula Ledzewicz, Heinz Schättler. Controlling a model for bone marrow dynamics in cancer chemotherapy. Mathematical Biosciences & Engineering, 2004, 1 (1) : 95-110. doi: 10.3934/mbe.2004.1.95 |
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Ariosto Silva, Alexander R. A. Anderson, Robert Gatenby. A multiscale model of the bone marrow and hematopoiesis. Mathematical Biosciences & Engineering, 2011, 8 (2) : 643-658. doi: 10.3934/mbe.2011.8.643 |
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Ana Isabel Muñoz, J. Ignacio Tello. On a mathematical model of bone marrow metastatic niche. Mathematical Biosciences & Engineering, 2017, 14 (1) : 289-304. doi: 10.3934/mbe.2017019 |
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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 |
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J. R. Fernández, R. Martínez, J. M. Viaño. Analysis of a bone remodeling model. Communications on Pure & Applied Analysis, 2009, 8 (1) : 255-274. doi: 10.3934/cpaa.2009.8.255 |
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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 |
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Sebastián Ferrer, Francisco Crespo. Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Journal of Geometric Mechanics, 2014, 6 (4) : 479-502. doi: 10.3934/jgm.2014.6.479 |
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Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic & Related Models, 2009, 2 (4) : 707-725. doi: 10.3934/krm.2009.2.707 |
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Manuel Delgado, Ítalo Bruno Mendes Duarte, Antonio Suárez Fernández. Nonlocal elliptic system arising from the growth of cancer stem cells. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1767-1795. doi: 10.3934/dcdsb.2018083 |
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Jaouad Danane, Karam Allali. Optimal control of an HIV model with CTL cells and latently infected cells. Numerical Algebra, Control & Optimization, 2020, 10 (2) : 207-225. doi: 10.3934/naco.2019048 |
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Faker Ben Belgacem. Uniqueness for an ill-posed reaction-dispersion model. Application to organic pollution in stream-waters. Inverse Problems & Imaging, 2012, 6 (2) : 163-181. doi: 10.3934/ipi.2012.6.163 |
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Christoph Sadée, Eugene Kashdan. A model of thermotherapy treatment for bladder cancer. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1169-1183. doi: 10.3934/mbe.2016037 |
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Chengjun Guo, Chengxian Guo, Sameed Ahmed, Xinfeng Liu. Moment stability for nonlinear stochastic growth kinetics of breast cancer stem cells with time-delays. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2473-2489. doi: 10.3934/dcdsb.2016056 |
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Robert Artebrant, Aslak Tveito, Glenn T. Lines. A method for analyzing the stability of the resting state for a model of pacemaker cells surrounded by stable cells. Mathematical Biosciences & Engineering, 2010, 7 (3) : 505-526. doi: 10.3934/mbe.2010.7.505 |
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Eugene Kashdan, Svetlana Bunimovich-Mendrazitsky. Multi-scale model of bladder cancer development. Conference Publications, 2011, 2011 (Special) : 803-812. doi: 10.3934/proc.2011.2011.803 |
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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 |
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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 |
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Alan D. Rendall. Multiple steady states in a mathematical model for interactions between T cells and macrophages. Discrete & Continuous Dynamical Systems - B, 2013, 18 (3) : 769-782. doi: 10.3934/dcdsb.2013.18.769 |
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Wenbo Cheng, Wanbiao Ma, Songbai Guo. A class of virus dynamic model with inhibitory effect on the growth of uninfected T cells caused by infected T cells and its stability analysis. Communications on Pure & Applied Analysis, 2016, 15 (3) : 795-806. doi: 10.3934/cpaa.2016.15.795 |
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Wei Feng, Shuhua Hu, Xin Lu. Optimal controls for a 3-compartment model for cancer chemotherapy with quadratic objective. Conference Publications, 2003, 2003 (Special) : 544-553. doi: 10.3934/proc.2003.2003.544 |
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