受媒体报道影响的SEIAQRS传染病模型分析

Analysis of SEIAQRS Epidemic Model Effected by Media Coverage

为深入了解新型冠状病毒肺炎的传播机制,建立了具有媒体报道和隔离的SEIAQRS传染病模型。利用基本再生数Rc讨论了平衡点的存在性与稳定性。当Rc<1时,无病平衡点是全局渐近稳定的,当Rc>1时,存在唯一的局部渐近稳定的地方病平衡点。分析了模型参数α(有症状感染者的隔离率)、p(有症状感染者的恢复率)和m0(媒体报道系数)对基本再生数的影响,发现隔离有症状感染者、提高有症状感染者的恢复率和加大常态化宣传传染病知识的媒体报道,能降低基本再生数Rc。最后,通过数值模拟验证了媒体报道和有效隔离能减少感染人数,进而有效控制新型冠状病毒肺炎的传播。

A SEIAQRS infectious disease model with media coverage and isolation is established to under‐stand the transmission mechanism of COVID-19.The existence and stability of equilibrium point are dis‐cussed by using the basic regeneration number Rc.When Rc<1,the disease-free equilibrium is globally asymptotically stable,and when Rc>1,there is a unique locally asymptotically stable endemic disease equilibrium.The effects of model parametersα(isolation rate of symptomatic infected persons),p(recov‐ery rate of symptomatic infected persons)and m0(media coverage coefficient)on the basic regeneration number are analyzed.It is obtained that isolating symptomatic infected persons,improving the recovery rate of symptomatic infected persons and increasing the media coverage of regular dissemination of infec‐tious disease knowledge can reduce the basic regeneration number Rc.Finally,through numerical simula‐tion,media coverage and effective isolation can greatly reduce the number of infected people,and thus effectively control the spread of COVID-19.