Medication and treatment are important measures for prevention and control of influenza. However, the benefit of antiviral use can be compromised if drug-resistant strains arise. Consequently, not only the epidemic size may increase with a higher level of treatment but also the viruses may become more resistant to the antiviral drugs. We use a mathematical model to explore the impact of antiviral treatment on the transmission dynamics of influenza. The model includes both drug-sensitive and -resistant strains.

Analytical and numerical results of the model show that the conventional quantity for the control reproduction number is not appropriate to use for gaining insights into the disease dynamics. We derive a new reproduction number by considering multiple generations of infection, and demonstrate that this new reproduction number provides a more reasonable measure for evaluating control programs as well as evolutionary implications of influenza medication strategies.