CHEN Lijun.Research on a stochastic epidemic model influenced by media information[J].Journal of Yanbian University,2024,(01):43-54.
受媒体信息影响的一类随机传染病模型的研究
- Title:
- Research on a stochastic epidemic model influenced by media information
- 文章编号:
- 1004-4353（2024）01-0043-12
- Keywords:
- stochastic SEIS epidemic model; nonlinear incidence rate; media information; persistence; extinction; stationary distribution
- 分类号:
- O175
- 文献标志码:
- A
- 摘要:
- 考虑到媒体信息对疾病预防和控制具有重要作用，建立了一类受媒体信息影响和具有非线性传染率的随机SEIS传染病模型，并运用随机微分方程的相关理论研究了该模型的绝灭性、持久性和平稳分布.数值模拟验证表明，当环境随机干扰越强或媒体信息报道得越及时时，传染病的绝灭速度越快.该研究结果改进和丰富了文献[12]的相关研究结果，并可为利用媒体信息进行预防和控制疾病提供良好参考.
- Abstract:
- Considering the important role of media for diseases prevention and control，a stochastic SEIS infectious disease model with media information and nonlinear infection rates was established. Moreover，correlation theories of stochastic differential equations were applied to investigate the extinction，persistence and stationary distribution issues of the model. Numerical simulation verifications showed that the stronger the random interference of the environment or the more effective media coverage，the rate of infectious disease extinction become the faster. The above results enriched and improved the research conclusions of reference [Journal of Northwest University(Natural Science Edition),2018,48(5):639-643]，and exhibit a good reference value for using media coverage to prevent and control diseases.
参考文献/References:
[1] KERMACK W O，MCKENDRICK A G. A contribution to the mathematical theory of epidemics[J]. Proceedings of the Royal Society of London. Series A，Containing Papers of a Mathematical and Physical Character，1927，115：700-721.
[2] LIU Q，JIANG D Q，SHI N Z. Threshold behavior in a stochastic SIQR epidemic model with standard incidence and regime switching[J]. Applied Mathematics and Computation，2018，316：310-325.
[3] LIU Q，JIANG D Q. Stationary distribution and extinction of a stochastic SIR model with nonlinear perturbation[J]. Applied Mathematics Letters，2017，73：8-15.
[4] LIU J M，CHEN L J，WEI F Y. The persistence and extinction of a stochastic SIS epidemic model with logistic growth[J]. Advances in Difference Equations，2018，2018：68.
[5] WEI F Y，RUI X. Stability and extinction of SEIR epidemic models with generalized nonlinear incidence[J]. Mathematics and Computers in Simulation，2020，170：1-15.
[6] 王娜.一类具有隔离项的时滞分数阶SIQ传染病模型的稳定性分析[J].延边大学学报(自然科学版)，2023，49(1)：36-42.
[7] LIU Q，JIANG D Q，SHI N Z，et al. Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence[J]. Physica A：Statistical Mechanics and its Applications，2016，462：870-882.
[8] WANG L W，ZHANG X A，LIU Z J. An SEIR epidemic model with relapse and general nonlinear incidence rate with application to media impact[J]. Qualitative Theory of Dynamical Systems，2018，17(2)：309-329.
[9] 王艳梅，刘桂荣. 具有信息干扰和Markov切换的随机传染病的灭绝性[J]. 山西大学学报(自然科学版)，2021， 44(2)：229-233.
[10] 朱霖河，黄晓媛. 具有媒体影响和时滞效应的传染病模型研究[J]. 数学的实践与认识，2021，51(2)：251-258.
[11] 张培钰，刘茂省.随机噪声和媒体报道影响的传染病模型分析[J].数学的实践与认识，2018，48(22)：186-194.
[12] 邢伟，高晋芳，颜七笙，等.一类受媒体报道影响的SEIS传染病模型的定性分析[J].西北大学学报(自然科学版)， 2018，48(5)：639-643.
[13] KHASMINSKII R. stochastic Stability of differential equations [M]. New York：Springer Science and Business Media， 2011.
备注/Memo
投稿日期：2023-11-03
基金项目：福建省中青年教师教育科研项目(JAT210662)；福建农林大学金山学院青年教师科研基金(kx230301)作者简介：陈丽君(1986— )，女，硕士，副教授，研究方向为非线性分析研究.