一类具有非线性扰动的新冠肺炎SIRC随机模型研究  

Research on a Class of COVID-19 SIRC Stochastic Model with Nonlinear Perturbation

作　　者：金薇 廖新元[1] 骆金鹏 杨永丽 Jin Wei;Liao Xinyuan;Luo Jinpeng;Yang Yongli(School of Mathematics and Physics,University of South China,Hengyang 421001,China)

机构地区：[1]南华大学数理学院,衡阳421001

出　　处：《数学理论与应用》2021年第1期1-11,共11页Mathematical Theory and Applications

摘　　要：考虑到环境噪声对目前流行的新冠肺炎有重大的影响,本文提出具有交叉免疫项的非线性扰动的随机SIRC模型并研究其随机性质.首先证明系统的随机最终有界性和随机持久性,然后通过建立合适的Lyapunov函数得到系统具有唯一遍历平稳分布和疾病灭绝的充分条件.最后通过数值模拟仿真验证以上结论,并比较在不同强度的噪声干扰下疾病灭绝的时间.结果表明干扰强度越大,越有利于疾病防控.Considering that the environmental noise has a significant impact on COVID-19, in this paper, a stochastic SIRC model of nonlinear perturbation with a cross immunity term is proposed and its stochastic properties are studied.First, the stochastic ultimate boundedness and stochastic persistence of the system are proved, and then some sufficient conditions for the unique ergodic stationary distribution of the system and the extinction of the disease are obtained by establishing an appropriate Lyapunov function. Finally, the above conclusions are verified by numerical simulations,and the extinction time of the disease under different intensities of noise is analyzed. The results show that the greater the intensity of noise interference, the more conducive to disease prevention and control.

关 键 词：非线性随机变量 随机最终有界性 遍历平稳分布 疾病持久与灭绝 

分 类 号：R563.1[医药卫生—呼吸系统] R181[医药卫生—内科学] O211.6[医药卫生—临床医学]