DYNAMICS OF A FILIPPOV AIRBORNE INFECTIOUS DISEASE MODEL WITH TRIPLE-THRESHOLD CONTROL STRATEGY

Filippov systems with single-threshold or double-threshold control strategies have been widely used to prevent and control airborne infectious diseases. A more realistic Filippov model with triple-threshold control strategy is proposed in this study to describe media coverage and quarantine measures triggered by the number of infections, as well as limited medical resources. Based on Filippov’s related theory and numerical analysis, we discuss the existence conditions of sliding segments and sliding dynamics, indicating that the repelling sliding segment and unstable pseudo-equilibrium may exist. Furthermore, we analyze the sliding bifurcations, including regular/virtual equilibrium bifurcation, boundary equilibrium bifurcation and grazing bifurcation. These bifurcations result in the emergence of tri-stability and globally stable limit cycle. Numerical analysis shows that when medical resources are sufficient, media coverage should be implemented as early as possible, while the implementation of quarantine measure relies on the global dynamics of the system. It also indicates that the effectiveness of quarantine measure does not always increase with stronger intensity of quarantine measure. Therefore, our study suggests that careful selection of appropriate threshold levels and control intensities is necessary so that the number of infections reach an ideal state.