In this paper, the dynamic behaviors are studied for a stochastic delayed avian influenza model with mutation and temporary immunity. First, we prove the existence and uniqueness of the global positive solution for the stochastic model. Second, we give two different thresholds ℛ01s and ℛ02s, and further establish the sufficient conditions of extinction and persistence in the mean for the avian-only subsystem and avian-human system, respectively. Compared with the corresponding deterministic model, the thresholds affected by the white noises are smaller than the ones of the deterministic system. Finally, numerical simulations are carried out to support our theoretical results. It is concluded that the vaccination immunity period can suppress the spread of avian influenza during poultry and human populations, while prompt the spread of mutant avian influenza in human population.

中文翻译：

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具有突变和暂时免疫的随机延迟禽流感模型的动力学

在本文中，研究了具有突变和暂时免疫的随机延迟禽流感模型的动态行为。首先，我们证明了随机模型全局正解的存在性和唯一性。其次，我们给出两个不同的阈值ℛ01s和ℛ02s, 并进一步分别建立了仅鸟类子系统和鸟类-人类系统均值中灭绝和持续存在的充分条件。与相应的确定性模型相比，白噪声影响的阈值小于确定性系统的阈值。最后，进行数值模拟以支持我们的理论结果。得出的结论是，疫苗免疫期可以抑制禽流感在禽类和人群中的传播，同时促进突变型禽流感在人群中的传播。