Optimal Disturbances of Bistable Time-Delay Systems Modeling Virus Infections

Abstract

For bistable time-delay dynamical systems modeling the dynamics of viral infections and the virusinduced immune response, an efficient approach is proposed for constructing optimal disturbances of steady states with a high viral load that transfer the system to a state with a low viral load. Functions approximating the behavior of drugs within the framework of well-known pharmacokinetic models are used as basis functions. Optimal disturbances are sought in the W₂¹ norm. It is shown that optimal disturbances found in this norm are superior to those found in the L₂ norm as applied to the development of adequate therapeutic strategies.