Existing mathematical progression models of hepatitis C virus (HCV) infection tend to have some limitations and often only study the effects of a few key factors on the progression. In this PhD research project, I developed a comprehensive mathematical disease progression model for HCV disease that considers the effect of control measures such as screening and treatment and that compares the effectiveness and costs of different testing strategies in relation to the presently used PCR testing for HCV screening in different settings. Such models allow us to conduct cost-effectiveness studies that can provide policymakers with more accurate information in order to make efficient resource allocation decisions. For instance, based on our model comparing screening strategies in Switzerland, we provided a recommendation on screening different population groups for HCV in Switzerland for the Federal Office of Public Health (FOPH) and found that only large-scale screening of the general population could substantially accelerate the rate of HCV diagnosis and treatment in Switzerland and other countries with similar epidemics. The details of this recommendation can be found on the official website of the FOPH. Moreover, our models suggested that screening strategies using an antigen test to diagnose HCV infection performed reasonably well in countries such as Georgia compared with the traditional antibody- and PCR-based approach.