A set-valued approach applied to a control problem of tuberculosis with treatment

Abstract

Abstract The objective of this paper is to propose a set-valued approach to handle the control problem of tuberculosis (TB) infection model with treatment. The governed model consists of four ordinary differential equations, namely, susceptible, latent, infected and treated individuals. The infectious TB groups are decreased to zero by using a Lyapunov function in the sense of viability theory. The corresponding control laws are given via a continuous selection of an adequately designed feedback map. Furthermore, minimal control is derived via minimal selection of the feedback map, despite its discontinuity. Ultimately, some numerical simulations are presented to show the efficiency of the set-valued approach.