A type of SEIR epidemic model with different general contact rates β1 (N) ,β2 (N) and β3 (N) , having infective force in all the latent ,infected and immune periods ,was studied .And the threshold ,basic reproductive number R0 which determines whether a disease is extinct or not ,was obtained .By using the Liapunov function method ,it was proved that the disease‐free equilibrium E0 is globally asymptotically stable and the disease eventually goes away if R0 <1 .It was also proved that in the case where R0 >1 ,E0 is unstable and the unique endemic equilibrium E* is locally asymptotically stable by Hurwitz criterion theory .It is show n that w hen disease‐induced death rate and elimination rate are zero ,the unique endemic equilibrium E* is globally asymptotically stable and the disease persists .%研究了一类具有不同一般形式的接触率β1（N），β2（N）和β3（N）且潜伏者，染病者和移出者均具有传染力的SEIR传染病模型，得到疾病流行与否的阈值———基本再生数 R0．运用Liapunov函数方法，证明了当 R0＜1时，无病平衡点 E0全局渐近稳定，疾病最终消失；利用 Hurwitz 判据定理，证明了当 R0＞1时，E0不稳定，地方病平衡点 E*局部渐近稳定；当因病死亡率和剔除率为零时，地方病平衡点 E*全局渐近稳定，疾病持续存在．
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