中文摘要：

考虑医院治疗的因素，给出了一个具有非线性发生率和非线性康复率的SEIR模型，讨论该模型的无病平衡点和地方病平衡点，证明向后分支的出现；进一步通过应用Lyapunov函数给出了它全局稳定性的分析。所得结果改进和扩展了文献中的相应结果。

英文摘要：

Considering the factor of hospital cure, an SEIR epidemic model with nonlinear incidence and nonlinear recovery rate is investigated. It is shown that the model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. A backward bifurcation leading to bistability possibly occurs. The global stability of the model is further studied by using the Lyapunov function. The corresponding results in literatures are improved and extended.