-
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), 39-58. |
[2] |
Ž. Bajzer, T. Carr, D. Dingli and K. Josić, Optimization of tumor virotherapy with recombinant measles viruses, Journal of Theoretical Biology, 252 (2008), 109-122.
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), 135-146. |
[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), 7293-7300.
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), 255-274.
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), 13-26.
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), 335-348.
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), 55-78.
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), 509.
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), 21.
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), 315-327.
doi: 10.1080/17513750903261281. |
[12] |
D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumor-immune interaction, Journal of Mathematical Biology, 34 (1998), 235-252.
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), 295-321. |
[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), 303-323.
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, 971-980. |
[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), 355-369.
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), 1094-1101.
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), 297-304.
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), 253-262.
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), 1-13.
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), 6628-6637.
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), 228.
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), 1307-1312. |
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), 39-58. |
[2] |
Ž. Bajzer, T. Carr, D. Dingli and K. Josić, Optimization of tumor virotherapy with recombinant measles viruses, Journal of Theoretical Biology, 252 (2008), 109-122.
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), 135-146. |
[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), 7293-7300.
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), 255-274.
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), 13-26.
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), 335-348.
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), 55-78.
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), 509.
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), 21.
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), 315-327.
doi: 10.1080/17513750903261281. |
[12] |
D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumor-immune interaction, Journal of Mathematical Biology, 34 (1998), 235-252.
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), 295-321. |
[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), 303-323.
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, 971-980. |
[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), 355-369.
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), 1094-1101.
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), 297-304.
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), 253-262.
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), 1-13.
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), 6628-6637.
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), 228.
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), 1307-1312. |
[1] |
Shigui Ruan. Nonlinear dynamics in tumor-immune system interaction models with delays. Discrete and 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 and Continuous Dynamical Systems - B, 2021, 26 (2) : 1149-1170. doi: 10.3934/dcdsb.2020157 |
[3] |
Urszula Ledzewicz, Mohammad Naghnaeian, Heinz Schättler. Dynamics of tumor-immune interaction under treatment as an optimal control problem. Conference Publications, 2011, 2011 (Special) : 971-980. doi: 10.3934/proc.2011.2011.971 |
[4] |
Lifeng Han, Changhan He, Yang Kuang. Dynamics of a model of tumor-immune interaction with time delay and noise. Discrete and Continuous Dynamical Systems - S, 2020, 13 (9) : 2347-2363. doi: 10.3934/dcdss.2020140 |
[5] |
Urszula Ledzewicz, Omeiza Olumoye, Heinz Schättler. On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth. Mathematical Biosciences & Engineering, 2013, 10 (3) : 787-802. doi: 10.3934/mbe.2013.10.787 |
[6] |
Martina Conte, Maria Groppi, Giampiero Spiga. Qualitative analysis of kinetic-based models for tumor-immune system interaction. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2393-2414. doi: 10.3934/dcdsb.2018060 |
[7] |
Min Yu, Gang Huang, Yueping Dong, Yasuhiro Takeuchi. Complicated dynamics of tumor-immune system interaction model with distributed time delay. Discrete and Continuous Dynamical Systems - B, 2020, 25 (7) : 2391-2406. doi: 10.3934/dcdsb.2020015 |
[8] |
Yangjin Kim, Hans G. Othmer. Hybrid models of cell and tissue dynamics in tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1141-1156. doi: 10.3934/mbe.2015.12.1141 |
[9] |
Giulio Caravagna, Alex Graudenzi, Alberto d’Onofrio. Distributed delays in a hybrid model of tumor-Immune system interplay. Mathematical Biosciences & Engineering, 2013, 10 (1) : 37-57. doi: 10.3934/mbe.2013.10.37 |
[10] |
J.C. Arciero, T.L. Jackson, D.E. Kirschner. A mathematical model of tumor-immune evasion and siRNA treatment. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 39-58. doi: 10.3934/dcdsb.2004.4.39 |
[11] |
Gladis Torres-Espino, Claudio Vidal. Periodic solutions of a tumor-immune system interaction under a periodic immunotherapy. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4523-4547. doi: 10.3934/dcdsb.2020301 |
[12] |
Sophia R-J Jang, Hsiu-Chuan Wei. On a mathematical model of tumor-immune system interactions with an oncolytic virus therapy. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 3261-3295. doi: 10.3934/dcdsb.2021184 |
[13] |
Urszula Ledzewicz, Mozhdeh Sadat Faraji Mosalman, Heinz Schättler. Optimal controls for a mathematical model of tumor-immune interactions under targeted chemotherapy with immune boost. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 1031-1051. doi: 10.3934/dcdsb.2013.18.1031 |
[14] |
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 and Continuous Dynamical Systems - B, 2021, 26 (10) : 5227-5249. doi: 10.3934/dcdsb.2020341 |
[15] |
Jianquan Li, Xiangxiang Ma, Yuming Chen, Dian Zhang. Complex dynamic behaviors of a tumor-immune system with two delays in tumor actions. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022033 |
[16] |
Dan Liu, Shigui Ruan, Deming Zhu. Bifurcation analysis in models of tumor and immune system interactions. Discrete and Continuous Dynamical Systems - B, 2009, 12 (1) : 151-168. doi: 10.3934/dcdsb.2009.12.151 |
[17] |
Jian-Guo Liu, Min Tang, Li Wang, Zhennan Zhou. Analysis and computation of some tumor growth models with nutrient: From cell density models to free boundary dynamics. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3011-3035. doi: 10.3934/dcdsb.2018297 |
[18] |
Elena Izquierdo-Kulich, Margarita Amigó de Quesada, Carlos Manuel Pérez-Amor, Magda Lopes Texeira, José Manuel Nieto-Villar. The dynamics of tumor growth and cells pattern morphology. Mathematical Biosciences & Engineering, 2009, 6 (3) : 547-559. doi: 10.3934/mbe.2009.6.547 |
[19] |
Yang Kuang, John D. Nagy, James J. Elser. Biological stoichiometry of tumor dynamics: Mathematical models and analysis. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 221-240. doi: 10.3934/dcdsb.2004.4.221 |
[20] |
Niklas Hartung. Efficient resolution of metastatic tumor growth models by reformulation into integral equations. Discrete and Continuous Dynamical Systems - B, 2015, 20 (2) : 445-467. doi: 10.3934/dcdsb.2015.20.445 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]