具有不连续控制策略的SIQR传染病模型的全局动力学分析

Global Dynamics of an SIQR Model with a Discontinuous Control Strategy

通过引入阈值控制策略,本文研究了一类分段光滑SIQR传染病模型的全局动力学.利用Filippov理论、非光滑Lyapunov函数、广义链式法则和Poincare映射等方法,讨论了无病平衡点、地方病平衡点和伪平衡点的全局渐近稳定性.特别地,得到了感染者数量全局有限时间收敛性结果,揭示了不连续动力系统的本质特征.借助数值仿真方法,阐述了所获理论结果的生物学意义,并为传染病的防控提供理论依据.

The objective of this paper is to investigate global dynamics of a piecewise smooth SIQR model with a threshold control strategy.By employing the approaches of Filippov theory,non-smooth Lyapunov functions,the generalized chain rule and Poincarémaps,we study the global asymptotical stability of a disease-free equilibrium,an endemic equilibria or a pseudo-equilibrium.Especially,some conditions are established to guarantee the global convergence in finite time of the number of the infected,which is an individual character of discontinuous dynamical systems.Making use of numerical simulations,the biological implications of the obtained results are presented and could help to control the infection.