Abstract: Near-optimization is important as optimization for theory of stochastic control and applications. In this work, we consider a stochastic viral model incorporating the lytic and nonlytic immune responses where the system is governed by stochastic differential equa- tions (SDE's). According to the adjoint equations, we estimate the error bound for the near optimality. Then, using the Hamiltonian function, Ekeland's variational principle and some basic estimates for state processes and adjoint processes , we will prove sufficient and necessary conditions to minimize the cost functional. Using control treatment, numerical illustrations are introduced to compare with theoretical.

Short biography: Mr. Driss Bouggar is a Ph.D. student at the Department of Mathematics, Faculty of sciences of Ibn Tofail University, Kénitra, Morocco. He works on stochastic optimal control theory and its applications in the fields of Virology, Epidemiology, and Oncology under the direction of Prof. Dr. Mohamed El Fatini. He received his master's degree in stochastics modeling and statistics at the university of Ibn Tofail in collaboration with Linnaeus University, Vaxjo, Sweden.