Estudio de algunos modelos en ecuaciones diferenciales relacionados con las terapias y las células madres

Abstract

The aim of this project is to analyze two models of ordinary differential equations with applications in medicine, particularly in the stem cells behaviour. The first model, introduced by Vladimir A. Kuznetsov & Mark A. Taylor, shows the competition between the immune system and cancer stem cells. The second model, introduced by D. Dingli & F. Michor, aims to research the behaviour of four types of stem cells: normal stem cells and tumor stem cells in reaction to the same type of cells but differentiated. In the course of this project, we will make a theoretical analysis in both models about the existence an uniqueness of solution, as well as a research of the steady states and their stability. Once we complete the theoretical analysis we will make numerical simulations to corroborate the obtained results and make conclusions for medicine applications.