具有饱和接触率的随机SIQS流行病模型的阈值动力学
Threshold Dynamics for the Stochastic SIQS Epidemic Model with Saturating Contact Rate
摘要: 本文描述和讨论了具有饱和接触率的随机SIQS模型。研究表明，可以通过一个阈值参数来确定模型的动力学。并且通过建立合适的李雅普诺夫函数，<我们证明了当Ros<1，疾病将灭绝；而Ros>1，疾病将持续存在。同时得到了平稳分布存在的一个充分条件。最后，数值模拟被用来阐述理论结果的合理性。
Abstract: In this paper, the stochastic SIQS model with saturating contact rate is characterized and discussed. The study shows that the dynamics of the model can be determined by a threshold parameter Ros. Moreover, by constructing suitable Lyapunov functions, we prove that the disease will die out when Ros<1; while Ros>1, the disease will be persistent. At the same time, a sufficient condition for the existence of stationary distribution is obtained. Finally, the reasonability of the theoretical results is confirmed by numerical simulations.
文章引用：许洁, 张天四. 具有饱和接触率的随机SIQS流行病模型的阈值动力学[J]. 应用数学进展, 2019, 8(11): 1827-1844. https://doi.org/10.12677/AAM.2019.811213

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