Human immunodeficiency virus (HIV) and hepatitis C virus (HCV) are potentially fatal chronic virus infections of public health importance. Whereas HCV can be cleared spontaneously in some infected individuals, HIV persists in the host but some patients can maintain long-term control of HIV replication during the chronic phase. The cellular immune response, and in particular the CD8+ T cell response, has been strongly associated to play a role in determining the outcome of both HIV and HCV infections. Nevertheless, there is conflicting evidence on the importance of CD8+ T cells in viral clearance or control and it remains unclear when, how and to what extent the CD8+ T cells interfere with viral replication. Mathematical modeling plays an important role in analyzing and interpreting clinical data of patients infected with HIV or HCV. The first part of this project deals with the analysis of four different data sets that cover particular aspects of HIV and HCV infection during the acute and chronic phase. By studying the viral turnover in different patients that are infected with HIV, and the occurrence of immune escape variants in HCV, the analyses will provide novel and fundamental insights into the viral dynamics and evolution within a host. In the second part, the insights from the data analysis will be used to develop new mathematical models of virus dynamics. This will help to conceptually study the factors that can influence the differential outcomes of HIV and HCV infections and test different hypotheses about the role of CD8+ T cells on the virus dynamics. The third part of the project deals with the evolution and spread of HIV variants that confer escape from CD8+ T cell recognition. Mathematical and computational models will be developed to study the rate at which such escape variants can spread at the population level, thereby anticipating the ongoing HIV epidemic. In summary, this project will provide new insights into how CD8+ T cells shape the viral dynamics and evolution, shedding more light on the controversial issue of the role of CD8+ T cells in suppressing viral replication. Ultimately, the newly gained insights into the role of CD8+ T cells to induce a selection pressure on the virus population, both within a host and at the population level, will be important for ongoing efforts in T-cell-based vaccine design for HIV and HCV.