A Two-Thresholds Policy for a Filippov Model in Combating Influenza

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.