dc.contributor Huguet Casades, Gemma dc.contributor Lázaro Ochoa, José Tomás dc.contributor.author Juan Meroño, Marcel dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2020-07-27T11:18:40Z dc.date.available 2020-07-27T11:18:40Z dc.date.issued 2020-07 dc.identifier.uri http://hdl.handle.net/2117/327724 dc.description.abstract Immunotherapy is a type of cancer treatment that boosts the natural defenses of the body to fight cancer without damaging normal cells. Many scientists have shown interest in developing a mathematical model that simulates the evolution of the populations of both immune and cancer cells under the effects of this treatment. In this project, we work with a couple of models of cancer dormancy proposed by Kathleen P. Wilkie and Philip Hanhnfeldt in their article "\emph{Mathematical models of immune-induced cancer dormancy and the emergence of immune evasion}". Using dynamical systems theory, we study the dynamics of a 3-dimensional system of differential equations that considers two different subpopulations of cancer cells: being one of them more resistant than the other against immune predation. We show that, if the predation strength of the immune cells against the cancer cells is constant, they will prevent the cancer population from escaping dormant state and only the more resistant subpopulation will survive. Moreover, using numerical integration, we study different modifications of a simple non-autonomous model assuming that the predation strength decays due to an immunoediting process. These modifications include some variations of a periodic treatment combined with immunotherapy. After comparing the results obtained from the modified models, we observe that all the solutions have similar values for both immune and cancer populations and that the different populations behave similarly in a three year interval. We conclude that these models may be too simple to represent accurately the evolution of an immune-induced cancer. dc.language.iso eng dc.publisher Universitat Politècnica de Catalunya dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics dc.subject.lcsh Dynamical systems dc.subject.lcsh Ergodic theory dc.subject.other Cancer dormancy dc.subject.other Mathematical model dc.subject.other Immunotherapy dc.title Population modelling for dormancy cancers dc.type Bachelor thesis dc.subject.lemac Sistemes dinàmics diferenciables dc.subject.lemac Teoria ergòdica dc.subject.ams Classificació AMS::37 Dynamical systems and ergodic theory dc.identifier.slug FME-2032 dc.rights.access Open Access dc.date.updated 2020-07-18T05:27:44Z dc.audience.educationlevel Grau dc.audience.mediator Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
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