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.

中文翻译：

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适用于结核病治疗控制问题的集值方法

本文的目的是提出一种集值方法来处理结核病 (TB) 感染模型与治疗的控制问题。治理模型由四个常微分方程组成，即易感个体、潜伏个体、感染个体和治疗个体。通过使用生存力理论意义上的李雅普诺夫函数，传染性 TB 组减少到零。通过连续选择适当设计的反馈图给出相应的控制规律。此外，最小控制是通过对反馈图的最小选择获得的，尽管它是不连续的。最后，提出了一些数值模拟来展示集值方法的效率。