-
Previous Article
Computational modeling approaches to studying the dynamics of oncolytic viruses
- MBE Home
- This Issue
-
Next Article
A flexible multivariable model for Phytoplankton growth
T model of growth and its application in systems of tumor-immune dynamics
1. | Department of Mathematical Sciences, Cameron University, Lawton, OK 73505 |
2. | School of Medicine, University of Alabama at Birmingham, Birmingham AL 35294 |
References:
[1] |
J. C. Arciero, T. L. Jackson and D. E. Kirschner, A mathematical model of tumor-immune evasion and siRNA treatment,, Discrete and Continuous Dynamical Systems-Series B, 4 (2004), 39.
|
[2] |
Ž. Bajzer, T. Carr, D. Dingli and K. Josić, Optimization of tumor virotherapy with recombinant measles viruses,, Journal of Theoretical Biology, 252 (2008), 109.
doi: 10.1016/j.jtbi.2008.01.016. |
[3] |
J. Burden, J. Ernstberger and K. R. Fister, Optimal control applied to immunotherapy,, Discrete and Continuous Dynamical Systems-Series B, 4 (2004), 135.
|
[4] |
A. Cappuccio, M. Elishmereni and Z. Agur, Cancer immunotherapy by Interleukin-21: Potential treatment strategies evaluated in a mathematical model,, Cancer Research, 66 (2006), 7293.
doi: 10.1158/0008-5472.CAN-06-0241. |
[5] |
F. Castiglione and B. Piccoli, Optimal control in a model of dendritic cell transfection cancer immunotherapy,, Bulletin of Mathematical Biology, 68 (2006), 255.
doi: 10.1007/s11538-005-9014-3. |
[6] |
A. d' Onofrio, U. Ledzewicz, H. Maurer and H. Schattler, On optimal delivery of combination therapy for tumors,, Mathematical Bioscience, 222 (2009), 13.
doi: 10.1016/j.mbs.2009.08.004. |
[7] |
H. P. de Vladar and J. A. González, Dynamic response of cancer under the influence of immunological activity and therapy,, Journal of Theoretical Biology, 227 (2004), 335.
doi: 10.1016/j.jtbi.2003.11.012. |
[8] |
D. Dingli, M. D. Cascino, K. Josić, S. J. Russell and Ž. Bajzer, Mathematical modeling of cancer radiovirotherapy,, Mathematical Biosciences, 199 (2006), 55.
doi: 10.1016/j.mbs.2005.11.001. |
[9] |
W. Eby, M. Tabatabai and Z. Bursac, Hyperbolastic modeling of tumor growth with a combined treatment of iodoacetate and dimethylsulfoxide,, BMC Cancer, 10 (2010).
doi: 10.1186/1471-2407-10-509. |
[10] |
M. S. Feizabadi and T. M. Witten, Chemotherapy in conjoint aging-tumor systems: some simple models for addressing coupled aging-cancer dynamics,, Theoretical Biology and Medical Modeling, 7 (2010).
doi: 10.1186/1742-4682-7-21. |
[11] |
I. Kareva, F. Berezovskaya and C. Castillo-Chavez, Myeloid cells in tumour-immune interactions,, Journal of Biological Dynamics, 4 (2010), 315.
doi: 10.1080/17513750903261281. |
[12] |
D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumor-immune interaction,, Journal of Mathematical Biology, 34 (1998), 235.
doi: 10.1007/s002850050127. |
[13] |
V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis,, Bulletin of Mathematical Biology, 56 (1994), 295. Google Scholar |
[14] |
U. Ledzewicz, H. Maurer and H. Schättler, Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy,, Mathematical Biosciences and Engineering, 8 (2011), 303.
doi: 10.3934/mbe.2011.8.307. |
[15] |
U. Ledzewicz, M. Naghnaeian and H. Schättler, "Dynamics of Tumor-Immune Interaction Under Treatment as an Optimal Control Problem,", Discrete and Continuous Dynamical Systems, (2011), 971.
|
[16] |
H. Schättler, U. Ledzewicz and B. Caldwell, Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis,, Mathematical Biosciences and Engineering, 8 (2011), 355.
doi: 10.3934/mbe.2011.8.355. |
[17] |
M. Simeoni, P. Magni, C. Cammia, G. De Nicolao, V. Croci, E. Pesenti, M. Germani, I. Pogessi and M. Rochetti, Predictive pharmokinetic-pharmodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents,, Cancer Research, 64 (2004), 1094.
doi: 10.1158/0008-5472.CAN-03-2524. |
[18] |
Y. Song, M.-M. Dong and H.-F. Yang, Effects of RNA interference targeting four different genes on the growth and proliferation of nasopharyngeal carcinoma CNE-2Z cells,, Cancer Gene Ther., 18 (2006), 297.
doi: 10.1038/cgt.2010.80. |
[19] |
M. Tabatabai, Z. Bursac, W. Eby and K. Singh, Mathematical modeling of stem cell proliferation,, Medical & Biological Engineering & Computation, 49 (2011), 253.
doi: 10.1007/s11517-010-0686-y. |
[20] |
M. Tabatabai, D. K. Williams and Z. Bursac, Hyperbolastic growth models: Theory and application,, Theoretical Biological and Medical Modeling, 2 (2005), 1.
doi: 10.1186/1742-4682-2-14. |
[21] |
A. Takeda, C. Goolsby and N. R. Yaseen, NUP98-HOXA9 induces long-term proliferation and blocks differentiation of primary human CD34+ hematopoietic cells,, Cancer Research, 66 (2006), 6628.
doi: 10.1158/0008-5472.CAN-06-0458. |
[22] |
K. Tao, M. Fang, J. Alroy and G. G. Sahagian, Imagable 4T1 model for the study of late stage breast cancer,, BMC Cancer, 8 (2008).
doi: 10.1186/1471-2407-8-228. |
[23] |
T. Yuri, R. Tsukamoto, K. Miki, N. Uehara, Y. Matsuoka and A. Tsubura, Biphasic effects of zeranol on the growth of estrogen receptor-positive human breast carcinoma cells,, Oncol. Rep., 16 (2006), 1307. Google Scholar |
show all references
References:
[1] |
J. C. Arciero, T. L. Jackson and D. E. Kirschner, A mathematical model of tumor-immune evasion and siRNA treatment,, Discrete and Continuous Dynamical Systems-Series B, 4 (2004), 39.
|
[2] |
Ž. Bajzer, T. Carr, D. Dingli and K. Josić, Optimization of tumor virotherapy with recombinant measles viruses,, Journal of Theoretical Biology, 252 (2008), 109.
doi: 10.1016/j.jtbi.2008.01.016. |
[3] |
J. Burden, J. Ernstberger and K. R. Fister, Optimal control applied to immunotherapy,, Discrete and Continuous Dynamical Systems-Series B, 4 (2004), 135.
|
[4] |
A. Cappuccio, M. Elishmereni and Z. Agur, Cancer immunotherapy by Interleukin-21: Potential treatment strategies evaluated in a mathematical model,, Cancer Research, 66 (2006), 7293.
doi: 10.1158/0008-5472.CAN-06-0241. |
[5] |
F. Castiglione and B. Piccoli, Optimal control in a model of dendritic cell transfection cancer immunotherapy,, Bulletin of Mathematical Biology, 68 (2006), 255.
doi: 10.1007/s11538-005-9014-3. |
[6] |
A. d' Onofrio, U. Ledzewicz, H. Maurer and H. Schattler, On optimal delivery of combination therapy for tumors,, Mathematical Bioscience, 222 (2009), 13.
doi: 10.1016/j.mbs.2009.08.004. |
[7] |
H. P. de Vladar and J. A. González, Dynamic response of cancer under the influence of immunological activity and therapy,, Journal of Theoretical Biology, 227 (2004), 335.
doi: 10.1016/j.jtbi.2003.11.012. |
[8] |
D. Dingli, M. D. Cascino, K. Josić, S. J. Russell and Ž. Bajzer, Mathematical modeling of cancer radiovirotherapy,, Mathematical Biosciences, 199 (2006), 55.
doi: 10.1016/j.mbs.2005.11.001. |
[9] |
W. Eby, M. Tabatabai and Z. Bursac, Hyperbolastic modeling of tumor growth with a combined treatment of iodoacetate and dimethylsulfoxide,, BMC Cancer, 10 (2010).
doi: 10.1186/1471-2407-10-509. |
[10] |
M. S. Feizabadi and T. M. Witten, Chemotherapy in conjoint aging-tumor systems: some simple models for addressing coupled aging-cancer dynamics,, Theoretical Biology and Medical Modeling, 7 (2010).
doi: 10.1186/1742-4682-7-21. |
[11] |
I. Kareva, F. Berezovskaya and C. Castillo-Chavez, Myeloid cells in tumour-immune interactions,, Journal of Biological Dynamics, 4 (2010), 315.
doi: 10.1080/17513750903261281. |
[12] |
D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumor-immune interaction,, Journal of Mathematical Biology, 34 (1998), 235.
doi: 10.1007/s002850050127. |
[13] |
V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis,, Bulletin of Mathematical Biology, 56 (1994), 295. Google Scholar |
[14] |
U. Ledzewicz, H. Maurer and H. Schättler, Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy,, Mathematical Biosciences and Engineering, 8 (2011), 303.
doi: 10.3934/mbe.2011.8.307. |
[15] |
U. Ledzewicz, M. Naghnaeian and H. Schättler, "Dynamics of Tumor-Immune Interaction Under Treatment as an Optimal Control Problem,", Discrete and Continuous Dynamical Systems, (2011), 971.
|
[16] |
H. Schättler, U. Ledzewicz and B. Caldwell, Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis,, Mathematical Biosciences and Engineering, 8 (2011), 355.
doi: 10.3934/mbe.2011.8.355. |
[17] |
M. Simeoni, P. Magni, C. Cammia, G. De Nicolao, V. Croci, E. Pesenti, M. Germani, I. Pogessi and M. Rochetti, Predictive pharmokinetic-pharmodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents,, Cancer Research, 64 (2004), 1094.
doi: 10.1158/0008-5472.CAN-03-2524. |
[18] |
Y. Song, M.-M. Dong and H.-F. Yang, Effects of RNA interference targeting four different genes on the growth and proliferation of nasopharyngeal carcinoma CNE-2Z cells,, Cancer Gene Ther., 18 (2006), 297.
doi: 10.1038/cgt.2010.80. |
[19] |
M. Tabatabai, Z. Bursac, W. Eby and K. Singh, Mathematical modeling of stem cell proliferation,, Medical & Biological Engineering & Computation, 49 (2011), 253.
doi: 10.1007/s11517-010-0686-y. |
[20] |
M. Tabatabai, D. K. Williams and Z. Bursac, Hyperbolastic growth models: Theory and application,, Theoretical Biological and Medical Modeling, 2 (2005), 1.
doi: 10.1186/1742-4682-2-14. |
[21] |
A. Takeda, C. Goolsby and N. R. Yaseen, NUP98-HOXA9 induces long-term proliferation and blocks differentiation of primary human CD34+ hematopoietic cells,, Cancer Research, 66 (2006), 6628.
doi: 10.1158/0008-5472.CAN-06-0458. |
[22] |
K. Tao, M. Fang, J. Alroy and G. G. Sahagian, Imagable 4T1 model for the study of late stage breast cancer,, BMC Cancer, 8 (2008).
doi: 10.1186/1471-2407-8-228. |
[23] |
T. Yuri, R. Tsukamoto, K. Miki, N. Uehara, Y. Matsuoka and A. Tsubura, Biphasic effects of zeranol on the growth of estrogen receptor-positive human breast carcinoma cells,, Oncol. Rep., 16 (2006), 1307. Google Scholar |
[1] |
Shigui Ruan. Nonlinear dynamics in tumor-immune system interaction models with delays. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 541-602. doi: 10.3934/dcdsb.2020282 |
[2] |
Shujing Shi, Jicai Huang, Yang Kuang. Global dynamics in a tumor-immune model with an immune checkpoint inhibitor. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1149-1170. doi: 10.3934/dcdsb.2020157 |
[3] |
Jianquan Li, Xin Xie, Dian Zhang, Jia Li, Xiaolin Lin. Qualitative analysis of a simple tumor-immune system with time delay of tumor action. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020341 |
[4] |
Laurence Cherfils, Stefania Gatti, Alain Miranville, Rémy Guillevin. Analysis of a model for tumor growth and lactate exchanges in a glioma. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020457 |
[5] |
Ebraheem O. Alzahrani, Muhammad Altaf Khan. Androgen driven evolutionary population dynamics in prostate cancer growth. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020426 |
[6] |
Zhimin Li, Tailei Zhang, Xiuqing Li. Threshold dynamics of stochastic models with time delays: A case study for Yunnan, China. Electronic Research Archive, 2021, 29 (1) : 1661-1679. doi: 10.3934/era.2020085 |
[7] |
Eric Foxall. Boundary dynamics of the replicator equations for neutral models of cyclic dominance. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1061-1082. doi: 10.3934/dcdsb.2020153 |
[8] |
Xueli Bai, Fang Li. Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3075-3092. doi: 10.3934/dcds.2020035 |
[9] |
Emre Esentürk, Juan Velazquez. Large time behavior of exchange-driven growth. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 747-775. doi: 10.3934/dcds.2020299 |
[10] |
Niklas Kolbe, Nikolaos Sfakianakis, Christian Stinner, Christina Surulescu, Jonas Lenz. Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 443-481. doi: 10.3934/dcdsb.2020284 |
[11] |
Anna Abbatiello, Eduard Feireisl, Antoní Novotný. Generalized solutions to models of compressible viscous fluids. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 1-28. doi: 10.3934/dcds.2020345 |
[12] |
Xin Guo, Lexin Li, Qiang Wu. Modeling interactive components by coordinate kernel polynomial models. Mathematical Foundations of Computing, 2020, 3 (4) : 263-277. doi: 10.3934/mfc.2020010 |
[13] |
Urszula Ledzewicz, Heinz Schättler. On the role of pharmacometrics in mathematical models for cancer treatments. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 483-499. doi: 10.3934/dcdsb.2020213 |
[14] |
P. K. Jha, R. Lipton. Finite element approximation of nonlocal dynamic fracture models. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1675-1710. doi: 10.3934/dcdsb.2020178 |
[15] |
João Marcos do Ó, Bruno Ribeiro, Bernhard Ruf. Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 277-296. doi: 10.3934/dcds.2020138 |
[16] |
Gabrielle Nornberg, Delia Schiera, Boyan Sirakov. A priori estimates and multiplicity for systems of elliptic PDE with natural gradient growth. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3857-3881. doi: 10.3934/dcds.2020128 |
[17] |
Claudia Lederman, Noemi Wolanski. An optimization problem with volume constraint for an inhomogeneous operator with nonstandard growth. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020391 |
[18] |
Patrick Martinez, Judith Vancostenoble. Lipschitz stability for the growth rate coefficients in a nonlinear Fisher-KPP equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 695-721. doi: 10.3934/dcdss.2020362 |
[19] |
Wei Feng, Michael Freeze, Xin Lu. On competition models under allee effect: Asymptotic behavior and traveling waves. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5609-5626. doi: 10.3934/cpaa.2020256 |
[20] |
Evelyn Sander, Thomas Wanner. Equilibrium validation in models for pattern formation based on Sobolev embeddings. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 603-632. doi: 10.3934/dcdsb.2020260 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]