Candy Sonveaux (Université de Namur)

Title:  “Vaccination strategy design by a state-feedback control for an Age-Dependent epidemiologic model”

An age-dependent SIR epidemic model is studied with an input corresponding to the vaccination rate of susceptible individuals. The stability analysis of the equilibria highlights that, when the basic reproduction number is greater than one, the endemic equilibrium is stable whereas the disease-free one is unstable. According to this result, we aim to design a stabilizing state-feedback law of vaccination which eradicates the disease. This law is obtained for two different models. The first one consists in a nonlinear set of ordinary differential equations derived from the second one, a set of nonlinear partial integro-differential equation (PIDE), via a discretization by age. For the first model, Isidori’s theory allows us to design a linearizing stabilizing state-feedback. The second law is deduced from the first one and, using similar arguments as in Isidori’s theory, we show that the application of this law to the PIDE model results in a linear, positive and stable closed-loop system. Moreover, non-negativity conditions for the feedback law are obtained in both cases, ensuring real feasibility of the control law. Finally, numerical simulations complement theoretical arguments.