This work designs a two-thresholds policy for a Filippov model in combating influenza, so as to estimate when and whether to take control strategies, including the media coverage, antiviral treatment of infected individuals and vaccination of susceptible population. By introducing two tolerance thresholds \(S_{c}\) and \(I_{c}\) of susceptible and infected individuals, the two-thresholds policy is designed as: a vaccination program is implemented when the number of susceptible individuals is above \(S_{c}\); an antiviral treatment strategy is taken and the mass media begins to report information about influenza when the infection number is larger than \(I_{c}\); no control strategies are required in other cases. Furthermore, the global dynamics of the model are analyzed by varying these two thresholds, including the existence and dynamics of sliding mode, and the existence and global stability of equilibrium. It is shown that the model solutions ultimately converge to a pseudoequilibrium or a pseudoattractor on the switching surface, or a real equilibrium. The obtained results indicate that, by choosing susceptible and infected thresholds properly, the infection number can be remained below or at an acceptable level.

这项工作为Filippov模型抗击流感设计了两个阈值的策略，以便估计何时以及是否采取控制策略，包括媒体报道，感染者的抗病毒治疗和易感人群的疫苗接种。通过引入易感和感染个体的两个容忍阈值\（S_ {c} \）和\（I_ {c} \），将两个阈值策略设计为：当易感个体的数量超过\（S_ {c} \） ; 当感染数量大于\（I_ {c} \）时，采取抗病毒治疗策略，大众媒体开始报告有关流感的信息; 在其他情况下，不需要控制策略。此外，通过改变这两个阈值来分析模型的全局动力学，包括滑动模式的存在和动力学以及平衡的存在和全局稳定性。结果表明，模型解最终收敛到切换面上的拟均衡或拟吸引子，或实际均衡。将所得到的结果表明，通过适当选择敏感和受感染的阈值时，感染数量可以保持低于或在可接受的水平。