一类考虑未就诊患者影响的传染病模型的动力学分析-《集美大学学报（自然科学版）》

文章信息/Info

Title:: Dynamic Analysis of a Class of Infectious Disease Model Considering the Influence of Nonclinic Visitors

Author(s):: MENG Hui; QI Longxing; (School of Mathematical Science,Anhui University,Hefei 230601,China)

Keywords:: basic reproduction number; nonclinic visitors; stability; Hopf bifurcation

摘要:: 考虑患者未就诊对疾病传播的影响，建立包含易感者、就诊患者和未就诊患者三维流行病传播模型。结果发现，疾病传播的基本再生数受到未就诊患者比例的影响，并证明了系统平衡点的存在性。通过构造Lyapunov函数证明了无病平衡点的全局渐近稳定性，分析地方病平衡点的局部渐近稳定性。当选取感染率作为分支参数时，系统在地方病平衡点处会出现Hopf分支现象。并且，利用规范型理论和中心流形定理，得到了Hopf分岔的方向和分支周期解的稳定性。

Abstract:: The influence of nonclinic visitors on disease transmission was considered,and a three-dimensional epidemic model involving susceptibles,outpatients and nonclinic visitors was established.In this paper,the basic reproduction number of the disease transmission was affected by the proportion of nonclinic visitors.The global asymptotic stability of the disease free equilibrium was proved by constructing the Lyapunov function,and the local asymptotic stability of the endemic equilibrium was analyzed.The nonclinic visitors could lead to complex dynamical behavior.When the transmission rate was selected to be the branching parameter,it was found that Hopf bifurcation occurs at the endemic equilibrium of the system.Furthermore,by using the normal form and center manifold theory,the direction of Hopf bifurcation and the stability of bifurcated periodic solutions were obtained.