一类包含媒体报道的SEQIHRS传染病模型的分析

Analysis of an SEQIHRS epidemic model with media coverage

研究了一类包含媒体报道与隔离措施的SEQIHRS传染病模型的动力学行为。首先得到了系统的有效再生数RC。其次,通过简单计算发现:系统总是存在无病平衡点,并且当RC<1时,它是局部渐近稳定的;当RC>1时,它是不稳定的。然后,运用中心流形定理,发现当域值RC通过1时,系统将会发生跨临界分支,并且唯一的地方病平衡点是局部渐近稳定的。此外,计算结果表明,被隔离个体的传染力将影响卫生部门如何实施相应的隔离措施。

An SEQIHRS epidemic model is proposed for the transmission dynamics of an infectious disease with quarantine and isolation control strategies. Firstly,we obtain the effective reproduction number RCof the system. Secondly,simple calculations indicate that the system always exists a disease-free equilibrium,and it is locally asymptotically stable if RC 1,whereas it is unstable if RC〉1.Thirdly,by use of central manifold theory,it is established that as RC passes through unity,transcritical bifurcation occurs in the system and the unique endemic equilibrium is asymptotically stable. In addition,mathematical results indicate that infectiousness of hospitalized individuals will determine howthe government takes control measures.