一类具有健康教育干预的Filippov手足口病模型

A Filippov HFMD Model with Health-Education Intervention

建立了一类Filippov模型刻画健康教育干预影响手足口病的过程:只有当感染人数超过阈值水平时,健康教育干预才会对传染率起到抑制作用;否则,健康教育干预不起效。研究了模型的滑动模式、滑动动力学以及各种平衡态的存在性。结果表明,当R0>1时,系统将稳定在两个子系统的地方病平衡态E1或E2或伪平衡态Es。这说明选取适当的实施健康教育干预的时机,可以将最终感染人数控制在一个事先给定的水平。

A Filippov model is formulated to describe the following real process of HFMD(hand-foot-mouth disease)with healtheducation intervention:once the case number exceeds the threshold level,the impact of health-education intervention on disease spreading occurs;otherwise,no impact exists for the case number below the threshold level.The sliding mode,sliding dynamics and all possible equilibria are examined.The main results show that the Filippov system will stabilize at one of the two endemic equilibria of the subsystems,i.e.,E1 or E2,or the pseudo-equilibrium Es for R0>1.It indicates that the number of infected indi⁃viduals can be stabilized at a previously given level if we implement health-education intervention properly.