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

作　　者：许洁 张天四[1] 

机构地区：[1]上海理工大学理学院,上海

出　　处：《应用数学进展》2019年第11期1827-1844,共18页Advances in Applied Mathematics

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,osos】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。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 Rosos>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.

关 键 词：SIQS流行病模型 饱和接触率 灭绝 持久性 平稳解 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]