Dynamics of Persistent Epidemic and Optimal Control of Vaccination

This talk is devoted to a model of epidemic progression, taking into account vaccination and immunity waning. The proposed model consists of a system of delay differential equations with time delays determined by the disease duration and immunity loss. Periodic epidemic outbreaks emerge as a result of the instability of a positive stationary solution if the basic reproduction number exceeds some critical value. Vaccination can change epidemic dynamics, resulting in more complex aperiodic oscillations, confirmed by some data on Influenza A in Norway. Optimal control allows for the minimization of epidemic cost by vaccination.