-
Previous Article
Ebola outbreak in West Africa: real-time estimation and multiple-wave prediction
- MBE Home
- This Issue
-
Next Article
Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering
Analysis of a cancer dormancy model and control of immuno-therapy
1. | Department of Mathematics, Iowa State University, Ames, IA 50011, United States, United States |
References:
[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.
doi: 10.1158/0008-5472.CAN-12-2447. |
[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.
doi: 10.1016/j.physd.2005.06.032. |
[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.
doi: 10.1007/s11538-010-9526-3. |
[5] |
J. Erler, et. al., Lysyl oxidase is essential for hypoxia-induced metastasis, Nature, 440 (2006), 1222-1226.
doi: 10.1038/nature04695. |
[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.
doi: 10.1109/TAC.1985.1104057. |
[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.
doi: 10.3934/dcdsb.2013.18.1031. |
[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.
doi: 10.1007/s00285-011-0424-6. |
[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.
doi: 10.1080/10428190400011625. |
[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.
doi: 10.1137/090749955. |
[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.
doi: 10.1038/nrc3236. |
[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.
doi: 10.1016/0005-1098(85)90099-8. |
[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), 7.
|
show all references
References:
[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.
doi: 10.1158/0008-5472.CAN-12-2447. |
[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.
doi: 10.1016/j.physd.2005.06.032. |
[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.
doi: 10.1007/s11538-010-9526-3. |
[5] |
J. Erler, et. al., Lysyl oxidase is essential for hypoxia-induced metastasis, Nature, 440 (2006), 1222-1226.
doi: 10.1038/nature04695. |
[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.
doi: 10.1109/TAC.1985.1104057. |
[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.
doi: 10.3934/dcdsb.2013.18.1031. |
[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.
doi: 10.1007/s00285-011-0424-6. |
[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.
doi: 10.1080/10428190400011625. |
[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.
doi: 10.1137/090749955. |
[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.
doi: 10.1038/nrc3236. |
[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.
doi: 10.1016/0005-1098(85)90099-8. |
[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), 7.
|
[1] |
Harsh Vardhan Jain, Avner Friedman. Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 945-967. doi: 10.3934/dcdsb.2013.18.945 |
[2] |
Baba Issa Camara, Houda Mokrani, Evans K. Afenya. Mathematical modeling of glioma therapy using oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 565-578. doi: 10.3934/mbe.2013.10.565 |
[3] |
Avner Friedman, Xiulan Lai. Free boundary problems associated with cancer treatment by combination therapy. Discrete and Continuous Dynamical Systems, 2019, 39 (12) : 6825-6842. doi: 10.3934/dcds.2019233 |
[4] |
Avner Friedman, Xiulan Lai. Antagonism and negative side-effects in combination therapy for cancer. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2237-2250. doi: 10.3934/dcdsb.2019093 |
[5] |
Danthai Thongphiew, Vira Chankong, Fang-Fang Yin, Q. Jackie Wu. An on-line adaptive radiation therapy system for intensity modulated radiation therapy: An application of multi-objective optimization. Journal of Industrial and Management Optimization, 2008, 4 (3) : 453-475. doi: 10.3934/jimo.2008.4.453 |
[6] |
Urszula Ledzewicz, Helen Moore. Optimal control applied to a generalized Michaelis-Menten model of CML therapy. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 331-346. doi: 10.3934/dcdsb.2018022 |
[7] |
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 |
[8] |
Marzena Dolbniak, Malgorzata Kardynska, Jaroslaw Smieja. Sensitivity of combined chemo-and antiangiogenic therapy results in different models describing cancer growth. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 145-160. doi: 10.3934/dcdsb.2018009 |
[9] |
Tania Biswas, Elisabetta Rocca. Long time dynamics of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2455-2469. doi: 10.3934/dcdsb.2021140 |
[10] |
Yangjin Kim, Avner Friedman, Eugene Kashdan, Urszula Ledzewicz, Chae-Ok Yun. Application of ecological and mathematical theory to cancer: New challenges. Mathematical Biosciences & Engineering, 2015, 12 (6) : i-iv. doi: 10.3934/mbe.2015.12.6i |
[11] |
Jerzy Klamka, Helmut Maurer, Andrzej Swierniak. Local controllability and optimal control for\newline a model of combined anticancer therapy with control delays. Mathematical Biosciences & Engineering, 2017, 14 (1) : 195-216. doi: 10.3934/mbe.2017013 |
[12] |
Cristian Morales-Rodrigo. A therapy inactivating the tumor angiogenic factors. Mathematical Biosciences & Engineering, 2013, 10 (1) : 185-198. doi: 10.3934/mbe.2013.10.185 |
[13] |
Amina Eladdadi, Noura Yousfi, Abdessamad Tridane. Preface: Special issue on cancer modeling, analysis and control. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : i-iii. doi: 10.3934/dcdsb.2013.18.4i |
[14] |
Shengqiang Liu, Lin Wang. Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy. Mathematical Biosciences & Engineering, 2010, 7 (3) : 675-685. doi: 10.3934/mbe.2010.7.675 |
[15] |
Manuel Delgado, Cristian Morales-Rodrigo, Antonio Suárez. Anti-angiogenic therapy based on the binding to receptors. Discrete and Continuous Dynamical Systems, 2012, 32 (11) : 3871-3894. doi: 10.3934/dcds.2012.32.3871 |
[16] |
Debra Lewis. Modeling student engagement using optimal control theory. Journal of Geometric Mechanics, 2022, 14 (1) : 131-150. doi: 10.3934/jgm.2021032 |
[17] |
Sibel Senan, Eylem Yucel, Zeynep Orman, Ruya Samli, Sabri Arik. A Novel Lyapunov functional with application to stability analysis of neutral systems with nonlinear disturbances. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1415-1428. doi: 10.3934/dcdss.2020358 |
[18] |
Jianjun Paul Tian. Finite-time perturbations of dynamical systems and applications to tumor therapy. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 469-479. doi: 10.3934/dcdsb.2009.12.469 |
[19] |
Rachid Ouifki, Gareth Witten. A model of HIV-1 infection with HAART therapy and intracellular delays. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 229-240. doi: 10.3934/dcdsb.2007.8.229 |
[20] |
Adam Glick, Antonio Mastroberardino. Combined therapy for treating solid tumors with chemotherapy and angiogenic inhibitors. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5281-5304. doi: 10.3934/dcdsb.2020343 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]