Mathematical models have been used to study the dynamics of HIV. Using these same principles, the dynamics of hepatitis C virus (HCV) are reviewed during interferon (IFN) therapy. After initiating IFN treatment, there is an IFN dose-dependent exponential decline in viral RNA levels within the first 48 hours. This rapid 1.0 to 2.0 log decline was best explained by an effect of IFN in inhibiting viral production with a varying degree of effectiveness. By applying mathematical principles, viral serum half-life was estimated to be 3.0 hours and viral production rat was calculated to be 1.0 x 10(12) virions per day. After this rapid first-phase decline there was a slower second phase decline in viral levels that was highly variable between subjects. This phase was dependent on the rate of elimination of HCV-infected liver cells. The rapidity of the second phase proved to be the best predictor of early viral clearance. The use of these models to understand the life cycle of viruses and their response to therapy is reviewed.