中文摘要：

针对现实中存在的非连续治疗现象,在已有连续治疗模型的基础上加入非连续免疫项h（y）,通过计算得到了模型的基本再生数R0,由微分包含的知识可以证明新模型存在2个平衡点.当R0〉1时,通过构造合适的Lyapunov函数,可证得满足初始条件的方程的解曲线在有限时间内全局收敛于地方平衡点;当R0〈1时,也可证得在有限时间内方程的解全局收敛于无病平衡点.文章最后运用MATLAB软件进行了数值模拟,模拟结果与理论结果一致.

英文摘要：

In view of the existence of discontnuous treatments, discontinuous h（y） was added into the present continuous treatment model. The basic reproductive number R0 was defined by the model equations, and the existence of two equilibrium were confirmed by the knowledge of differential inclusion. When R0 〉1, through a suitable Lyapunov function the global convergence to the disease equilibrium was accompolished in finite time;if R0 〈1, the global convergence to the disease-free equilibrium could also be obtained in finite time. The results were in consistent with the numerical simulation results of MATLAB.