一类具有非线性发病率的随机传染病模型的持久性  

On Persistence for a Stochastic Epidemic Model with Nonlinear Incidence

作　　者：李艳 储家蕊 廖新元[1] LI Yan;CHU Jiarui;LIAO Xinyuan(School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China)

机构地区：[1]南华大学数理学院,湖南衡阳421001

出　　处：《南华大学学报（自然科学版）》2023年第1期71-77,共7页Journal of University of South China：Science and Technology

摘　　要：本文研究了一类具有非线性发病率的SIS随机模型。首先对其相应的确定性模型进行了平衡态稳定性分析,得到了决定疾病灭绝和持久存在的阈值;然后利用随机微分方程的一些理论对随机系统在环境噪声影响下的阈值进行了研究;最终得到了疾病在随机系统中灭绝和持久存在的充分条件,并用数值模拟验证了所得结论的正确性。In this paper,a SIS stochastic model with nonlinear incidence rate is studied.Firstly,the equilibrium stability analysis of its corresponding deterministic model is carried out,and the threshold that determines the extinction and existence of diseases is obtained;and then the threshold of stochastic system under the influence of environmental noise is studied by some theories of stochastic differential equations.Finally the sufficient conditions for the extinction and persistence of diseases in stochastic systems are obtained,and the correctness of the obtained conclusions is verified by numerical simulation.

关 键 词：随机微分方程 平衡稳定性 灭绝性 持久性 

分 类 号：O211.63[理学—概率论与数理统计]