一类具有媒体效应的时滞SSIIR模型稳定性定量分析

Quantitative analysis of stability for a delayed epidemic model with media effects

将易感者人群划分为普通的易感者S与有意识的易感者SI,建立了一类具有媒体效应的SSIIR时滞传染病模型.通过计算该模型的基本再生数,对其平衡点的存在性和稳定性进行了论证;证明了疾病持久性的充分条件,对参数进行了局部敏感性分析,最后进行了数值模拟.数据模拟结果显示,媒体效应所诱导的时滞τ存在临界值τ_(0),当τ<τ_(0)时,地方病平衡点保持稳定,在τ>τ0时出现Hopf分支并出现分支周期解;人群S向SI的转换率λ越大疾病越快得到控制,而S与SI对疾病的认知偏差程度K的增加则会不利于疾病的控制.因此,媒体应尽力向大众传达准确且具有时效性的信息,以便尽快控制疾病的传播.

In the report,the susceptible population was divided into ordinary susceptible population S and con-scious susceptible population SI and a delayed epidemic model with media coverage SSIIR was established.Based on the basic regeneration number of the model,the existence and stability of its equilibrium point were demonstrated;The sufficient condition of disease persistence was proved,and the local sensitivity analysis of pa-rameters was performed.Finally,numerical simulation was carried out.The results showed that there is a criti-cal valueττ_(0) for the time lag of media reportsτ.Whenτ<ττ_(0),the balance point of endemic disease remains stable.Whenτ>τ0,Hopf bifurcations and bifurcated periodic solutions begin to appear.The bigger theλ,the conver-sion rate from population S to population SI,the faster the disease will be controlled.The increase of K,the cog-nitive bias of these two populations,will be detrimental to the control of the disease.Therefore,the media should try their best to convey accurate and timely information to the public,so as to control the spread of dis-ease as soon as possible.