有干预措施的Filippov戒烟模型的全局动力学

Global Dynamics of a Filippov Smoking Cessation Model with Interventions

考虑到媒体和政府对吸烟的不连续干预策略,在经典传染病模型的基础上,建立了一类有干预措施的Filippov戒烟模型.利用Filippov定性分析方法,分析了模型的滑模动力学和全局动力学行为.在不同的参数区域,得到了系统无病平衡点、地方病平衡点或伪平衡点的全局渐近稳定性.结果说明适当的干预能够降低吸烟人数并将吸烟人数控制在阈值之内.

Considering the discontinuous intervention strategies on smoking by the media and government,based on the infectious disease model,a Filippov smoking cessation model with interventions is established.Making use of the method of Filippov qualitative analysis,we investigate its sliding mode dynamics and further global dynamics.By varying the parameters,it is shown that the Filippov system stabilizes at a unique equilibrium which is a disease-free equilibrium,an endemic equilibrium or a pseudo-equilibrium.The results indicate that appropriate interventions can reduce the number of smokers and keep them within a predetermined threshold level.