标题： 随机动力学与具有环境噪声的广义流行病模型的概率分析 显示英文标题

标题： Stochastic Dynamics and Probability Analysis for a Generalized Epidemic Model with Environmental Noise

摘要： 本文我们考虑一个具有广义传染率函数的随机SEIQR（易感-暴露-感染-隔离-恢复）流行病模型。 利用Lyapunov方法，我们建立了该模型全局正解的存在性和唯一性，确保其随时间保持定义良好。 通过应用Young不等式和切比雪夫不等式，我们证明了随机最终有界性和随机持久性的概念，提供了在随机扰动下流行病动态长期行为的见解。 此外，我们推导了随机灭绝的条件，描述了流行病可能最终消失的情况，以及V-几何遍历性，表明系统状态收敛到平衡点的速度。 最后，我们进行了数值模拟以验证我们的理论结果，并评估不同参数下模型的行为。 显示英文摘要

摘要： In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniqueness of a global positive solution to the model, ensuring that it remains well-defined over time. Through the application of Young's inequality and Chebyshev's inequality, we demonstrate the concepts of stochastic ultimate boundedness and stochastic permanence, providing insights into the long-term behavior of the epidemic dynamics under random perturbations. Furthermore, we derive conditions for stochastic extinction, which describe scenarios where the epidemic may eventually die out, and V-geometric ergodicity, which indicates the rate at which the system's state converges to its equilibrium. Finally, we perform numerical simulations to verify our theoretical results and assess the model's behavior under different parameters.