Lyapunov函数在一类随机扰动的SIS-VS传染病系统中的应用
|
摘要
考虑一类具有随机扰动的SIS-VS传染病系统,应用新的Lyapunov函数研究该系统的遍历性,得到了该随机传染病系统平稳分布存在性和遍历性的充分条件.结果表明,Lyapunov函数的构造方法改进了依赖于确定性模型的地方病平衡点和疾病致死率限制的已有结果,得到了更适用的条件.
We considered a class of SIS-VS epidemic system with random perturbation,applied the new Lyapunov function to study the ergodicity of the system,and obtained the sufficient conditions for the existence and ergodicity of the stationary distribution of the stochastic epidemic system.The results show that the construction method of Lyapunov function improves the existing results of endemic equilibrium and the mortality,which depend on the deterministic models,and obtains more applicable conditions.
We considered a class of SIS-VS epidemic system with random perturbation,applied the new Lyapunov function to study the ergodicity of the system,and obtained the sufficient conditions for the existence and ergodicity of the stationary distribution of the stochastic epidemic system.The results show that the construction method of Lyapunov function improves the existing results of endemic equilibrium and the mortality,which depend on the deterministic models,and obtains more applicable conditions.
引文
[1] ZHAO Yanan,JIANG Daqing.Dynamics of Stochastically Perturbed SIS Epidemic Model with Vaccination[J/OL].Abstr Appl Anal,2013-07-12.doi:10.1155/2013/517439.
[2] Tornatore E,Vetro P,Buccellato S M.SIVR Epidemic Model with Stochastic Perturbation[J].Neural Comput Appl,2014,24(2):309-315.
[3] Gray A,Greenhalgh D,Hu L,et al.A Stochastic Differential Equation SIS Epidemic Model[J].SIAM J Appl Math,2011,71(3):876-902.
[4] YANG Qingshan,JIANG Daqing,SHI Ningzhong,et al.The Ergodicity and Extinction of Stochastically Perturbed SIR and SEIR Epidemic Models with Saturated Incidence[J].J Math Anal Appl,2012,388(1):248-271.
[5] Lahrouz A,Omari L.Extinction and Stationary Distribution of a Stochastic SIRS Epidemic Model with Non-linear Incidence[J].Statist Probab Lett,2013,83(4):960-968.
[6] Hening A,Nguyen D H,Yin G.Stochastic Population Growth in Spatially Heterogeneous Environments:The Density-Dependent Case[J].J Math Biol,2018,76(3):697-754.
[7] Nguyen D H,Yin G.Modeling and Analysis of Switching Diffusion Systems:Past-Dependent Switching with a Countable State Space[J].SIAM J Control Optim,2016,54(5):2450-2477.
[8] LI Jianquan,MA Zhien.Global Analysis of SIS Epidemic Models with Variable Total Population Size[J].Math Comput Modelling,2004,39(11/12):1231-1242.
[9] Hasminskii R Z.Stochastic Stability of Differential Equations[M].2nd ed.Berlin:Springer,2012.
[2] Tornatore E,Vetro P,Buccellato S M.SIVR Epidemic Model with Stochastic Perturbation[J].Neural Comput Appl,2014,24(2):309-315.
[3] Gray A,Greenhalgh D,Hu L,et al.A Stochastic Differential Equation SIS Epidemic Model[J].SIAM J Appl Math,2011,71(3):876-902.
[4] YANG Qingshan,JIANG Daqing,SHI Ningzhong,et al.The Ergodicity and Extinction of Stochastically Perturbed SIR and SEIR Epidemic Models with Saturated Incidence[J].J Math Anal Appl,2012,388(1):248-271.
[5] Lahrouz A,Omari L.Extinction and Stationary Distribution of a Stochastic SIRS Epidemic Model with Non-linear Incidence[J].Statist Probab Lett,2013,83(4):960-968.
[6] Hening A,Nguyen D H,Yin G.Stochastic Population Growth in Spatially Heterogeneous Environments:The Density-Dependent Case[J].J Math Biol,2018,76(3):697-754.
[7] Nguyen D H,Yin G.Modeling and Analysis of Switching Diffusion Systems:Past-Dependent Switching with a Countable State Space[J].SIAM J Control Optim,2016,54(5):2450-2477.
[8] LI Jianquan,MA Zhien.Global Analysis of SIS Epidemic Models with Variable Total Population Size[J].Math Comput Modelling,2004,39(11/12):1231-1242.
[9] Hasminskii R Z.Stochastic Stability of Differential Equations[M].2nd ed.Berlin:Springer,2012.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |