中文摘要：

讨论了一个具有一般饱和传染率及两种控制措施SIRS传染病模型,分析了模型平衡点的稳定性态,并通过构造Lyapunov函数得到了地方病平衡点的全局稳定性.同时,本研究探讨了对易感者和染病者通过降低传染率和提高恢复率进行管理控制的最优措施,利用最优控制理论分析了一定时间内使染病者人数最少同时所投入经济成本最低的控制措施和管理方法,对疾病流行时实施最优控制的效果进行了数值模拟,结果显示当采取治疗等管理措施后,疾病由流行逐渐得到控制,直至最终绝灭.

英文摘要：

A SIRS epidemic model with saturated incidence and optimal control is discussed the stabilities of the equilibria are analyzed and the global stability of the endemic equilibrium is proved by constructing a Lyapunov function. At the same time,this paper deals with the optimal measures to carry out management and control over the susceptibles and infections through reducing the infectivity and improving the recovery rate. The optimal control theory is used to analyze the control measure and management method for the least number of the infections andminimuminput economic cost within a certain time. The numberical simulation is made4 of the effect of implementing the optimal control when the incidence occurs. The results indicate that after the cure and management measures are adopted, the prevalence rate of the diseases is gradually controlled till to their extinction.