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Mathematical Biosciences and Engineering (MBE)
 

Analysis of a cancer dormancy model and control of immuno-therapy
Pages: 1037 - 1053, Issue 5, October 2015

doi:10.3934/mbe.2015.12.1037      Abstract        References        Full text (2010.9K)           Related Articles

Ben Sheller - Department of Mathematics, Iowa State University, Ames, IA 50011, United States (email)
Domenico D'Alessandro - Department of Mathematics, Iowa State University, Ames, IA 50011, United States (email)

1 A. M. Baker, et. al., Lysyl Oxidase Plays a Critical Role in Endothelial Cell Stimulation to Drive Tumor Angiogenesis, Cancer Research, 73 (2013), 583-594.
2 A. D'Onofrio, A general framework for modeling tumor-immune system competition and immuno-therapy, mathematical analysis and biomedical inferences, Physica D, 208 (2005), 220-235.       
3 G. P. Dunn, L. J. Old and R. D. Schreiber, The three E's of cancer immuno-editing, Annu. Rev. Immunol., 22 (2004), 329-360.
4 R. Eftimie, J. L. Bramson and D. J. Earn, Interactions between the immune systems and cancer: A brief review of non-spatial mathematical models, Bull. Math. Biol., 73 (2011), 2-32.       
5 J. Erler, et. al., Lysyl oxidase is essential for hypoxia-induced metastasis, Nature, 440 (2006), 1222-1226.
6 R. Genesio, M. Tartaglia and A. Vicino, On the estimation of asymptotic stability regions: State of the art and new proposals, IEEE Transactions on Automatic Control, 30 (1985), 747-755.       
7 W. Hahn, Stability of Motion, Springer Verlag, Heidelberg-Berlin, 1967.       
8 T. Kailath, Linear Systems, Prentice-Hall Information and System Sciences Series. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1980.       
9 M. Krstić, I. Kanellakopoulos and P. V. Kokotović, Nonlinear and Adaptive Control Design, John Wiley and Sons, 1995.
10 V. A. Kuznetsov, Mathematical modeling of the development of dormant tumors and immune stimulation of their growth, Cybern. syst. Anal, 23 (1988), 556-564.
11 V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis, Bull. Math. Biol, 56 (1994), 295-321.
12 U. Ledzewicz, M. Faraji and H. Schaettler, Mathematical model of tumor-immune interactions under chemotherapy with immune boost, Discrete and Continuous Dynamical Systems, Series B, 18 (2013), 1031-1051.       
13 U. Ledzewicz, M. Naghneian and H. Schaettler, Optimal response to chemotherapy for a mathematical model of tumor-immune dynamics, Journal of Mathematical Biology, 64 (2012), 557-577.       
14 L. Norton and R. Simon, Growth curve of an experimental solid tumor following radiotherapy, J. of the National Cancer Institute, 58 (1977), 1735-1741.
15 L. Norton, A Goempertzian model of human breast cancer growth, Cancer Research, 48 (1988), 7067-7071.
16 K. Page and J. Uhr, Mathematical models of cancer dormancy, Leukemia and Lymphoma, 46 (2005), 313-327.
17 G. Phan et. al., Cancer regression and autoimmunity induced by cytotoxic T lymphocyte-associated antigen 4 blockade in patients with metastatic melanoma, PNAS, 100 (2003), 8372-8377.
18 S. Ratschan and Z. She, Providing a basin of attraction to a target region of polynomial systems by computation of Lyapunov-like functions, SIAM J. Control Optim., 48 (2010), 4377-4394.       
19 S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence and Robustness, Prentice-Hall, Advanced Reference Series (Engineering), 1989.
20 A. Scott, J. Wolchock and L. Old, Antibody therapy of cancer, Nature Reviews Cancer, 12 (2012), 278-287.
21 N. V. Stepanova, Course of the immune reaction during the development of a malignant tumor, Biophysics, 24 (1980), 917-923.
22 T. Takayanagi, H. Kawamura and A. Ohuchi, Cellular automaton model of a tumor tissue consisting of tumor cells, cytoxic T lymphocytes (CTLs), and cytokine produced by CTLs, IPSJ Trans Math Model Appl., 47 (2006), 61-67.
23 A. Vannelli and M. Vidyasagar, Maximal Lyapunov functions and domains of attraction for autonomous nonlinear systems, Automatica, 21 (1985), 69-80.       
24 K. P. Wilkie, A Review of Mathematical Models of Cancer-Immune Interactions in the Context of Tumor Dormancy, Systems Biology of Tumor Dormancy, Springer, New York, 2013.
25 V. I. Zubov, Mathematical Methods for the Study of Automatic Control Systems, Israel Jerusalem Academic Press, 1962.       
26 V. I. Zubov, Methods of A.M. Lyapunov and Their Application, the Netherlands, Noordhoff, 1964.       
27 Sydney International Workshop on Math Models of Tumor-Immune System Dynamics, January 7-10, 2013.

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