摘要
建立一类具有非单调传染率的SIQR随机传染病模型。利用停时理论,证明了该模型全局解的存在唯一性;通过Liapunov函数方法并结合伊藤公式,讨论了随机系统的解在相应确定模型的无病平衡点附近的振荡行为,并且得到了该模型的灭绝性和存在唯一平稳分布的充分条件。最后,数值模拟显示了模型的解与相应的确定性模型解的渐近行为的差异。
A stochastic SIQR epidemic model with nonmonotonic transmission rate is formulated.The existence and uniqueness of global solution to the model are obtained by using the stopping time theory.By using the Liapunov function method and the Ito’s formula,the oscillation behavior of the solutions of the stochastic model near the disease-free equilibrium point of the corresponding deterministic model is discussed.Sufficient conditions for the extinction and the existence of a unique stationary distribution are obtained.Finally,the numerical simulations results show the difference of asymptotic behavior between the model solution and the corresponding deterministic model solution.
作者
马苓涓
张太雷
李志民
MA Lingjuan;ZHANG Tailei;LI Zhimin(School of Science,Chang’an University,Xi’an 710064,China)
出处
《南昌大学学报（理科版）》
CAS
北大核心
2020年第6期515-523,共9页
Journal of Nanchang University(Natural Science)
基金
国家自然科学基金资助项目(11701041)
陕西省自然科学基础研究计划(2018JM1011)。
关键词
随机传染病模型
伊藤公式
平稳分布
灭绝性
Stochastic epidemic model
Ito’s formula
Disease extinction
Stationary distribution
