Acoplamento de modelos computacionais de doenças infecciosas

Abstract

The development of mathematical models of the immune response allows a better understanding of the multifaceted mechanisms of this defense system. The main purpose of this work is to represent different scales and aspects of the host-pathogen interaction during infection and treatment by the coupling of distinct mathematical models. Two examples are defined. On the first example the local tissue inflammation processes are described by Partial Differential Equations (PDEs) whereas a system of Ordinary Differential Equations (ODEs) is used as a model for the systemic response. The simulation of distinct scenarios allows the analysis of the dynamics of different immune cells in the presence of a bacteria. It was shown with the qualitative analysis of the results of the coupled model that the systemic response is essential to eliminate the bacteria. In the second example a set of ordinary differential equations representing infection of the hepatitis C virus (HCV) is coupled to a set of partial differential equations that was developed to represent intracellular dynamics. That example allowed the study of HCV replication under therapy using direct acting antiviral drugs (DAAs) and was validated comparing to experimental data. The results support that with the coupling of computational models, other mathematical analysis and simulations could be performed, in a reasonable time frame, aiding to the study of the complex immune system and the development of treatment to infections.