Um Modelo Espacial para a Resposta Imunológica Adaptativa da Hepatite B

• Autor(a) principal: Pieri, Karen [UNESP]
• Data de Publicação: 2010
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/120570
• topic: Hepatite B; Resposta imune; Modelos matematicos

This paper proposed a two-dimensional spatial model to describe the adaptive immune response for viral hepatitis B. This model considered six populations: healthy hepatocytes T, infected hepatocytes Y , hepatitis B virus V , innate immune system I, active immune system X and memory cells, X. First, a compartmental model was constructed and its equilibrium solutions and also the threshold values related to the stability of each solution were obtained. Using this model, we was able to reproduce the different trends observed for the disease, which are: individuals that eliminate the infection without forming immune response, patients with acute and chronic carriers. By including dispersion of defense cells of the immune system and virus (spatial model), we analyze two situations: homogeneous model, in which the model parameters are the same at all points of the network, and heterogeneous model, which characterizes cells more permeable and less permeable to virus invasion. For the two spatial models (homogeneous and heterogeneous) the times relatead to the viral erradication and/or virus invasion and persistence becoming smaller in relation to the compartmental model. The results also showed that for the set of values used in the simulations and if the two diffusion rates are different from zero, the model is sensitive to variations in the rate of viral spread and not dependent on the dispersion of memory cells. Finally, the heterogeneous model when compared to the homogeneous model shows that the infection can be spatially limited depending on the type of the cell involved in the infection process