Dinamica populacional do sistema imune aplicada ao sararmpo / Population dynamics of the immune system applied to measles

AUTOR(ES)
DATA DE PUBLICAÇÃO

2010

RESUMO

This work is a study of the interaction between the measles virus and the human immune system from the point of view of the population dynamics. Dynamical systems of first order non linear ordinary differential equations are used to model this population dynamics. Because of the fact that it is possible to observe two different and quite distinct moments in the infection by the measles virus, we chose to develop two different mathematical models in order to accurately describe the whole process of infection. The first model describes the early stage of the infection and the second model describes the second stage of the infection, the systemic phase. Both these models are developed and studied in the first two chapters. We have calculated the trivial equilibrium points of these models and we have studied their stability. More over, we have studied the non trivial equilibrium points and have determined its existence, uniqueness and stability. We show many graphics from numerical simulations of the behaviour of both models. In these simulations we have used a certain set of parameters which were chosen in accordance with the threshold condition (local stability criteria). In these graphics we can observe variations in the immune responses weaker or stronger. In the third chapter we have studied both models connected, we made a comparision between the cellular response and the humoral response effectiveness and, eventually, we made a few considerations about the relation between measles and malnutrition

ASSUNTO(S)

biomatemática imunologia modelos matematicos sistemas dinamicos simulação virus do sarampo biomathematics immunology mathematical models dynamical systems simulation measles virus

ACESSO AO ARTIGO

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