中文摘要：

文章研究了具非连续治疗策略的传染病模型,在合理的猜想之下,通过构造相应的Lyapunov函数证明了模型在有限时间内全局收敛于平衡点,当R0〉1时,建立一个Lyapunov函数来证明系统在有限时间内全局收敛于地方病平衡点;当R0〈1时,同样证明了系统在有限时间内全局收敛于无病平衡点.所得的结果改进和扩展了文献中的相应结论.

英文摘要：

A SIRS epidemic model with discontinuous therapy strategy is proposed in this paper. Under some reasonable suppositions,it is proved that the model achieves global convergence to the equilibrium point in finite time by Lyapunov function. If R0 1,a corresponding Lyapunov function is established to prove the system achieves global convergence to the endemic equilibrium in finite time. If R0 1,it is also proved that the system achieves global convergence to the disease free equilibrium in finite time.The results improve and extend the corresponding conclusions in the literature.