A fraction of chronic hepatitis C patients treated with direct‐acting antivirals (DAAs) achieved sustained virological responses (SVR), or cure, despite having detectable viremia at the end of treatment (EOT). This observation, termed EOT
+/SVR, remains puzzling and precludes rational optimization of treatment durations. One hypothesis to explain EOT
+/SVR, the immunologic hypothesis, argues that the viral decline induced by DAAs during treatment reverses the exhaustion of cytotoxic T lymphocytes (CTLs), which then clear the infection after treatment. Whether the hypothesis is consistent with data of viral load changes in patients who experienced EOT
+/SVR is unknown. Here, we constructed a mathematical model of viral kinetics incorporating the immunologic hypothesis and compared its predictions with patient data. We found the predictions to be in quantitative agreement with patient data. Using the model, we unraveled an underlying bistability that gives rise to EOT
+/SVR and presents a new avenue to optimize treatment durations. Infected cells trigger both activation and exhaustion of CTLs. CTLs in turn kill infected cells. Due to these competing interactions, two stable steady states, chronic infection and viral clearance, emerge, separated by an unstable steady state with intermediate viremia. When treatment during chronic infection drives viremia sufficiently below the unstable state, spontaneous viral clearance results post‐treatment, marking EOT
+/SVR. The duration to achieve this desired reduction in viremia defines the minimum treatment duration required for ensuring SVR, which our model can quantify. Estimating parameters defining the CTL response of individuals to HCV infection would enable the application of our model to personalize treatment durations.