中文摘要：

研究一类具反馈控制和标准发生率的SI传染病模型,运用常微分方程平衡点的理论,证明了该系统无病平衡点的全局渐近稳定性和局部渐近稳定性.通过构造适当的Lyapunov函数,证明了该系统染病平衡点的局部渐近稳定性,给出疾病趋于消失或地方性流行的一个充分条件.最后通过数值模拟验证了所得结论的正确性.

英文摘要：

This paper studies an epidemic model with model feedback controls and standard incidence. Using the balance theory of ordinary differential equ＇ations, it proves that the system is global asymptotic stability of the disease-free equilibrium and the locally asymptotic stability. By constructing suitable Lyapunov function, it also proves that the system have the locally asymptotic stability of the equilibrium. A sufficient condition is given for the disease to disappear or endemic. Finally, numerical simulation verifies the validity of the main results.