Séminaire Cristiana Silva

Lundi 16 septembre 2019 (16h00, Salle G001)

Cristiana Silva, University of Aveiro, Portugal.

Titre : Optimal control of HIV transmission: from compartmental to in-host models.

Résumé : We propose and analyse mathematical models for HIV transmission both form the epidemiological and in-host point of view. Time delays are introduced to the previous models and the stability of equilibrium points is studied. An optimal control problem is proposed and analysed, where HIV treatment and immunotherapy are described by two control functions, subject to time-delays. In addition the process is subject to a state constraint on the number of effector cells. The main goal is to find the optimal combination of HIV treatment and immunotherapy that maximizes the concentration of uninfected $CD4^+ T$ cells and immune response cells (CTL) and keep the side effects as low as possible. A necessary optimality conditions of the Maximum Principle for time-delayed optimal control problems with state constraints is discussed. In particular, we obtain an explicit formula of the multiplier associated with the state constraint. Solutions for the non-delayed and delayed control problem are computed numerically, applying discretisation and nonlinear programming methods.