Mathematical model for the competitive interaction between cancer cells and the immune system with cancer therapy
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A simple mathematical model is presented that consists of a system of two ordinary differential equations (ODEs), applicable to the interaction between cancer cells, the immune system and a photodynamic therapy based on the previous observations of the Physicochemical Research Group of Bio and Nanomaterials of the Universidad del Valle (Basante et al., 2016, Basante, 2017) where an exponential effect is assumed. The consequences of the treatment are analyzed based on the stability analysis of the dynamic system, finding that it is possible to find adequate conditions for the elimination of cancer.
Rubén Camargo, Universidad del Valle, Facultad de Ingeniería, Escuela de Ingeniería Química, Cali, Colombia
https://orcid.org/0000-0003-0640-0104
Jesús A. Mesa-Zora, Universidad del Valle, Facultad de Ingeniería, Escuela de Ingeniería Química, Cali, Colombia
https://orcid.org/0000-0001-5440-3970
Ignacio Barradas, Centro de Investigación en Matemáticas CIMAT, Guanajuato, México
https://orcid.org/0000-0002-5973-9200
Basante-Romo, Mónica J., Oscar Gutierrez, and Rubén J. Camargo-Amado. "Evaluacion de la Citotoxicidad Inducida por TIO2 modificado Funcionalizado con Folato y Oro sobre Lineas Celulares de HeLa y CHO." Información tecnológica 27.5 (2016): 63-68. DOI: https://doi.org/10.4067/S0718-07642016000500008
Basante M. J. Mecanismo de acción de terapia fotodinámica para cáncer con TiO2 modificado en células Hela y sus efectos en modelo animal. Tesis doctoral. Universidad del Valle; 2017.
Boyce, W. E., DiPrima, R. C., & Meade, D. B. Elementary differential equations. John Wiley & Sons; 2017.
Chrobak, J. M., & Herrero, H. Un modelo matemático de competición entre cáncer y sistema inmune. In XXI Congreso de Ecuaciones Diferenciales y Aplicaciones y XI Congreso de Matemática Aplicada CEDYA; 2009.
de Pillis, Lisette G., Ami E. Radunskaya, and Charles L. Wiseman. "A validated mathematical model of cell-mediated immune response to tumor growth." Cancer research 65.17 (2005): 7950-7958. DOI: https://doi.org/10.1158/0008-5472.CAN-05-0564
Díaz, J. I., Tello, J. I. On the mathematical controllability in a simple growth tumors model by the internal localized action of inhibitors Nonlinear Analysis: Real World Applications. 2003;4:109-125. DOI: https://doi.org/10.1016/S1468-1218(02)00017-2
Gałach, M. Dynamics of the Tumor---Immune System Competition---the Effect of Time Delay. International Journal of Applied Mathematics and Computer Science. 2003;13:395-406.
Hart, D., E. Shochat, and Z. Agur. "The growth law of primary breast cancer as inferred from mammography screening trials data." British journal of cancer 78.3 (1998): 382-387. DOI: https://doi.org/10.1038/bjc.1998.503
Hirsch, M. W., Smale, S., & Devaney, R. L. Differential equations, dynamical systems, and an introduction to chaos. Academic press; 2012. DOI: https://doi.org/10.1016/B978-0-12-382010-5.00015-4
Jones, D. S., Plank, M., & Sleeman, B. D. Differential equations and mathematical biology. 2009; CRC press. DOI: https://doi.org/10.1201/9781420083583
Kirschner, D., & Panetta, J. C. (1998). Modeling immunotherapy of the tumor–immune interaction. Journal of mathematical biology, 37(3), 235-252. DOI: https://doi.org/10.1007/s002850050127
Kuznetsov, Vladimir A., et al. "Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis." Bulletin of mathematical biology 56.2 (1994): 295-321. DOI: https://doi.org/10.1016/S0092-8240(05)80260-5
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