受媒体信息影响的一类随机传染病模型的研究  

Research on a stochastic epidemic model influenced by media information

作　　者：陈丽君[1] CHEN Lijun(Jin Shan College,Fujian Agriculture and Forestry University,Fuzhou 350002,China)

机构地区：[1]福建农林大学金山学院,福州350002

出　　处：《延边大学学报（自然科学版）》2024年第1期43-54,共12页Journal of Yanbian University（Natural Science Edition）

基　　金：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)。

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。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.

关 键 词：随机SEIS传染病模型 非线性传染率 媒体信息 持久性 绝灭性 平稳分布 

分 类 号：O175[理学—数学]