Population persistence and extinction are the most important issues in ecosystems. In the past a few decades, various deterministic and stochastic mathematical models with Allee effect have been extensively studied. However, in both population and disease dynamics, the question of how structural transitions caused by internal or external environmental noise emerge has not been fully elucidated. In this paper, we introduce a semi-analytical method to explore the asymptotically convergent behavior of a stochastic avian influenza model with Allee effect. First, by introducing noise to the model, we observe numerically a significant transition from bistability to monostability. Next, a corresponding Fokker-Planck (FPK) equation is obtained to analytically describe the probability density distributions with long time evolution in order to reveal the transition characteristics. Ratio of the approximately convergent probabilities for the two key equilibria derived from the FPK equation confirms the stability transition observed by previous numerical simulations. Moreover, bifurcation analysis in two important parameters demonstrates that noise not only reduces the parametric zone of sustaining bistability but also drives the system to exhibit different monostabilities, which correspond numerically to population persistence and extinction at different parametric intervals, respectively. Furthermore, noise induces higher probabilities for the system to sustain persistence instead of extinction in this model. Our results could provide some suggestions to improve wildlife species survival in more realistic situations where noise exists.

人口的持久性和灭绝是生态系统中最重要的问题。在过去的几十年中，对具有Allee效应的各种确定性和随机数学模型进行了广泛的研究。但是，在人口和疾病动力学方面，尚未完全阐明由内部或外部环境噪声引起的结构转变如何出现的问题。在本文中，我们引入一种半分析方法来探索具有Allee效应的随机禽流感模型的渐近收敛行为。首先，通过将噪声引入模型，我们在数值上观察到了从双稳态到单稳态的重大转变。下一个，得到一个对应的福克-普朗克方程（FPK），以分析描述长时间演化的概率密度分布，以揭示过渡特征。从FPK方程得出的两个关键平衡点的近似收敛概率之比证实了先前的数值模拟所观察到的稳定性转变。此外，在两个重要参数上的分叉分析表明，噪声不仅降低了维持双稳态的参数区域，而且驱使系统表现出不同的单稳态，这在数值上分别对应于在不同参数间隔的种群持续存在和灭绝。此外，在此模型中，噪声引起系统维持持久性而不是灭绝的更高概率。