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Modelos de interacción entre células tumorales y el sistema inmune

dc.contributor.advisorCarpio, Ana
dc.contributor.authorGallardo Arroyo, Carlos
dc.date.accessioned2023-06-18T01:50:05Z
dc.date.available2023-06-18T01:50:05Z
dc.date.defense2017
dc.date.issued2017
dc.degree.titleGrado en matermáticas
dc.description.abstractEste trabajo de grado es un acercamiento a modelos dinámicos basados en ecuaciones diferenciales con los cuales poder modelizar la interacción entre las células tumorales y el sistema inmune. Haremos un recorrido por distintos modelos planteados a lo largo de los últimos años de una, dos y tres ecuaciones estudiando algunas de sus características, tanto de forma cualitativa como analítica. También haremos algunas simulaciones numéricas que nos ayudarían a entender cómo funcionan estos modelos.
dc.description.abstractThis end-of-degree paper is an approach to dynamic models based on differential equations with which to model the interaction between tumor cells and the immune system. We will take a tour of some different models proposed over the last years of one, two and three equations studying some of their characteristics, both qualitatively and analytically. We will also do some numerical simulations that will help us understand how these models work.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedFALSE
dc.description.statusunpub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/73608
dc.identifier.urihttps://hdl.handle.net/20.500.14352/20932
dc.language.isospa
dc.rights.accessRightsopen access
dc.subject.cdu517.9
dc.subject.cdu612.017
dc.subject.cdu616-006.04
dc.subject.keywordCáncer
dc.subject.keywordSistema inmune
dc.subject.keywordCitoquinas
dc.subject.keywordEcuaciones diferenciales
dc.subject.keywordBifurcaciones
dc.subject.keywordSimulación
dc.subject.keywordDiagrama de fases
dc.subject.keywordCancer
dc.subject.keywordDifferential equations
dc.subject.keywordInmune system
dc.subject.keywordCytokinas
dc.subject.keywordBifurcations
dc.subject.keywordSimulation
dc.subject.keywordPhase portrait
dc.subject.ucmMatemáticas (Matemáticas)
dc.subject.ucmAnálisis matemático
dc.subject.ucmOncología
dc.subject.unesco12 Matemáticas
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.subject.unesco3201.01 Oncología
dc.titleModelos de interacción entre células tumorales y el sistema inmune
dc.typebachelor thesis
dcterms.references[1] Interactions Between the Immune System and Cancer: A Brief Review of Non-spatial Mathematical Models. Eftimie, R., Bramson, J.L. and Earn, D.J.D. Bull. Math. Biol. (2011) 73: 2 [2] Araujo, R., McElwain, D., 2004. A history of the study of solid tumor growth: the contribution of mathematical modeling. Bull. Math. Biol. 66, 1039{1091. [3] Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis, A. Carpio, G. Duro, Nonlinear Analysis-Real World Applications 30, 184-212, 2016 [4] Modelizacion y simulacion en sistemas dinámicos, A. Carpio, 2017, eprints.ucm.es [5] Bellomo, N., Delitala, M., 2008. From the mathematical kinetic, and stochastic game theory to modeling mutations, onset, progression and immune competition of cancer cells. Phys. Life Rev. 5, 183{206. [6] von Bertalanfly, L., 1957. Quantitative laws in metabolism and growth. Q. Rev. Biol. 32, 217-231. [7] Hart, D., Shochat, E., Agur, Z., 1998. The growth law of primary breast cancer as inferred from mammography screening trials data. Br. J. Cancer 78, 382-387. [8] Laird, A., 1964. Dynamics of tumor growth. Br. J. Cancer 18, 490-502. [9] Bifurcation Analysis of Tumor-Immune ODE System L.G. de Pillis and A.E. Radunskaya; August 15, 2002 [10] Norton, L., 1988. A Gompertzian model of human breast cancer growth. Cancer Res. 48, 7067{7071. [11] d'Onofrio, A., 2008. Metamodeling tumor-immune system interaction, tumor evasion and immunotherapy. Math. Comput. Model. 47, 614-637. [12] d'Onofrio, A., 2005. A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences. Physica D 208, 220-235. [13] Kuznetsov, V., Makalkin, I., Taylor, M., Perelson, A., 1994. Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math. Biol. 2(56), 295-321. [14] Sotolongo-Costa, O., Molina, L.M., Perez, D.R., Antoraz, J., Reyes, M.C., 2003. Behavior of tumors under nonstationary therapy. Physica D 178, 242-253. [15] Moore, H., Li, N., 2004. A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction. J. Theor. Biol. 227, 513-523. [16] de Pillis, L., Radunskaya, A., 2003a. The dynamics of an optimally controlled tumor model: a case study. Math. Comput. Model. 37, 1221-1244. [17] Kirschner, D., Panetta, J., 1998. Modeling immunotherapy of the tumor-immune interaction. J. Math. Biol. 37, 235{252. [18] Owen, M., Sherratt, J., 1998. Modeling the macrophage invasion of tumors: effects on growth and composition. Math. Med. Biol. 15, 165-185.
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