Made available in DSpace on 2015-03-26T13:45:35Z (GMT). No. of bitstreams: 1 texto completo.pdf: 1273195 bytes, checksum: f2a08950868ce92e14d235d207851dde (MD5) Previous issue date: 2013-07-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this dissertation we study concepts and results about dynamical systems with emphasis at Butler-McGehee Lemma. The purpose of this work is to introduce and to prove three versions of Butler-McGehee Lemma, as well as, two applications of this lemma. Such applications deal with the behavior of solutions to the systems of Ordinary Differential Equations that describe populations of species that interact in the same environment. The adopted conditions show that in the system with two species, one specie is going to extinguish and another is going to survive with constant population. In the system with three species there is coexistence among the species. The Butler-McGehee Lemma has been found to be an efficient tool that helps to acquire information about the regions of attraction and repulsion of certain sets. / Nesta dissertação estudam-se conceitos e resultados de sistemas dinâmicos com ênfase no Lema de Butler-McGehee. O objetivo é apresentar e demonstrar três versões do Lema de Butler-McGehee, bem como, duas aplicações deste lema. Tais aplicações tratam da análise global do comportamento de soluções de sitemas de equações diferenciais ordinárias que representam as populações de espécies que interagem num mesmo ambiente. Com as condições adotadas, para o sistema com duas espécies mostra-se que uma das espécies é extinta e a outra tende a se manter constante. Já no sistema com três espécies mostra-se que há a coexistência entre as três espécies. Conclui-se que o Lema de Butler-McGehee é uma ferrramenta eficiente que auxilia na obtenção de informações a cerca das regiões de atração e repulsão de determinados conjuntos.

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Human T-lymphotropic virus type I (HTLV-I) is a persistent human retrovirus characterized by life-long infection and risk of developing HAM/TSP, a progressive neurological and inflammatory disease. Despite extensive studies of HTLV-I, a complete understanding of the viral dynamics has been elusive. Previous mathematical models are unable to fully explain experimental observations. Motivated by a new hypothesis for the mechanism of HTLV-I infection, a three dimensional compartmental model of ordinary differential equations is constructed that focusses on the highly dynamic interactions among populations of healthy, latently infected, and actively infected target cells. Results from mathematical and numerical investigations give rise to relevant biological interpretations. Comparisons of these results with experimental observations allow us to assess the validity of the original hypothesis. Our findings provide valuable insights to the infection and persistence of HTLV-I in vivo and motivate future mathematical and experimental work. / Applied Mathematics