A delayed SEIR epidemic model with saturated incidence and saturated treatment function is considered in this paper. Sufficient conditions for the existence of local Hopf bifurcation are established by regarding the possible combination of the two delays as the bifurcation parameter. General formula for the direction, period and stability of the bifurcated periodic solutions are derived by using the normal form method and the centre manifold theory. Finally, some numerical simulations are given to illustrate the obtained results.

中文翻译：

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具有饱和发生率和饱和治疗功能的延迟SEIR流行病模型的分叉分析。

考虑具有饱和发生率和饱和治疗功能的时滞SEIR流行病模型。通过将两个延迟的可能组合作为分叉参数，为存在局部Hopf分叉的充分条件建立了条件。利用范式和中心流形理论推导了分叉周期解的方向，周期和稳定性的一般公式。最后，给出了一些数值模拟来说明所获得的结果。