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Discrete & Continuous Dynamical Systems - B

February 2004 , Volume 4 , Issue 1

Mathematical Models in Cancer

A special issue based on the Cancer Workshop at Vanderbilt University 2002
Guest Editors: Mary Ann Horn and Glenn Webb

This special issue is featured in Economist, one of the most influential publications

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Inside mathematical modeling: building models in the context of wound healing in bone
John A. Adam
2004, 4(1): 1-24 doi: 10.3934/dcdsb.2004.4.1 +[Abstract](996) +[PDF](221.0KB)
Growth kinetics of cancer cells prior to detection and treatment: An alternative view
Evans K. Afenya and Calixto P. Calderón
2004, 4(1): 25-28 doi: 10.3934/dcdsb.2004.4.25 +[Abstract](1036) +[PDF](83.3KB)
Hopf point analysis for angiogenesis models
Zvia Agur, L. Arakelyan, P. Daugulis and Y. Ginosar
2004, 4(1): 29-38 doi: 10.3934/dcdsb.2004.4.29 +[Abstract](918) +[PDF](139.4KB)
A mathematical model of tumor-immune evasion and siRNA treatment
J.C. Arciero, T.L. Jackson and D.E. Kirschner
2004, 4(1): 39-58 doi: 10.3934/dcdsb.2004.4.39 +[Abstract](1127) +[PDF](372.7KB)
From a class of kinetic models to the macroscopic equations for multicellular systems in biology
N. Bellomo and A. Bellouquid
2004, 4(1): 59-80 doi: 10.3934/dcdsb.2004.4.59 +[Abstract](1420) +[PDF](209.3KB)
Macrophage-tumour interactions: In vivo dynamics
H.M. Byrne, S.M. Cox and C.E. Kelly
2004, 4(1): 81-98 doi: 10.3934/dcdsb.2004.4.81 +[Abstract](971) +[PDF](210.0KB)
A mathematical model of BCR-ABL autophosphorylation, signaling through the CRKL pathway, and Gleevec dynamics in chronic myeloid leukemia
Pep Charusanti, Xiao Hu, Luonan Chen, Daniel Neuhauser and Joseph J. DiStefano III
2004, 4(1): 99-114 doi: 10.3934/dcdsb.2004.4.99 +[Abstract](990) +[PDF](281.0KB)
The steady state of a maturity structured tumor cord cell population
Janet Dyson, Rosanna Villella-Bressan and G.F. Webb
2004, 4(1): 115-134 doi: 10.3934/dcdsb.2004.4.115 +[Abstract](1198) +[PDF](213.0KB)
Optimal control applied to immunotherapy
Thalya Burden, Jon Ernstberger and K. Renee Fister
2004, 4(1): 135-146 doi: 10.3934/dcdsb.2004.4.135 +[Abstract](1216) +[PDF](166.3KB)
A hierarchy of cancer models and their mathematical challenges
Avner Friedman
2004, 4(1): 147-159 doi: 10.3934/dcdsb.2004.4.147 +[Abstract](1233) +[PDF](135.6KB)
Modelling cell populations with spatial structure: Steady state and treatment-induced evolution
Alessandro Bertuzzi, Alberto d'Onofrio, Antonio Fasano and Alberto Gandolfi
2004, 4(1): 161-186 doi: 10.3934/dcdsb.2004.4.161 +[Abstract](839) +[PDF](406.3KB)
A mathematical model of prostate tumor growth and androgen-independent relapse
T.L. Jackson
2004, 4(1): 187-201 doi: 10.3934/dcdsb.2004.4.187 +[Abstract](1443) +[PDF](384.6KB)
On the stability of homogeneous solutions to some aggregation models
R. Kowalczyk, A. Gamba and L. Preziosi
2004, 4(1): 203-220 doi: 10.3934/dcdsb.2004.4.203 +[Abstract](999) +[PDF](631.8KB)
Biological stoichiometry of tumor dynamics: Mathematical models and analysis
Yang Kuang, John D. Nagy and James J. Elser
2004, 4(1): 221-240 doi: 10.3934/dcdsb.2004.4.221 +[Abstract](1097) +[PDF](237.3KB)
A model of tumor and lymphocyte interactions
Amy H. Lin
2004, 4(1): 241-266 doi: 10.3934/dcdsb.2004.4.241 +[Abstract](1266) +[PDF](1427.8KB)
Modeling the role of angiogenesis in epidermal wound healing
Sophia A. Maggelakis
2004, 4(1): 267-273 doi: 10.3934/dcdsb.2004.4.267 +[Abstract](1180) +[PDF](370.9KB)
Evaluation of a discrete dynamic systems approach for modeling the hierarchical relationship between genes, biochemistry, and disease susceptibility
Jason H. Moore and Lance W. Hahn
2004, 4(1): 275-287 doi: 10.3934/dcdsb.2004.4.275 +[Abstract](802) +[PDF](122.3KB)
Dynamics of a model for brain tumors reveals a small window for therapeutic intervention
Kristin R. Swanson, Ellsworth C. Alvord, Jr and J. D. Murray
2004, 4(1): 289-295 doi: 10.3934/dcdsb.2004.4.289 +[Abstract](876) +[PDF](132.2KB)
Stochastic modeling of carcinogenesis: State space models and estimation of parameters
W. Y. Tan, L.-J. Zhang and C.W. Chen
2004, 4(1): 297-322 doi: 10.3934/dcdsb.2004.4.297 +[Abstract](911) +[PDF](589.5KB)
Unraveling the complexity of cell cycle effects of anticancer drugs in cell populations
Paolo Ubezio
2004, 4(1): 323-335 doi: 10.3934/dcdsb.2004.4.323 +[Abstract](1066) +[PDF](226.2KB)
A free boundary problem model of ductal carcinoma in situ
Yongzhi Xu
2004, 4(1): 337-348 doi: 10.3934/dcdsb.2004.4.337 +[Abstract](1013) +[PDF](149.7KB)

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