一类考虑先天免疫和非线性治愈率的时滞传染病模型Hopf分岔  

Hopf Bifurcation of a Delayed Epidemic Model Considering Innate Immunity and Nonlinear Cure Rate

作　　者：张子振[1] 张怡雪 ZHANG Zizhen;ZHANG Yixue(School of Management Science and Engineering,Anhui University of Finance and Economics,Bengbu 233030,China)

机构地区：[1]安徽财经大学管理科学与工程学院,安徽蚌埠233030

出　　处：《山东航空学院学报》2024年第4期115-120,共6页Journal of Binzhou University

基　　金：国家自然科学基金项目(12001001)。

摘　　要：考虑到传染病流行过程中先天免疫对个体的重要性,研究了一类具有先天免疫和非线性治愈率的时滞SEIS传染病模型。以感染者恢复所需要的时间周期时滞为分岔参数,通过讨论模型特征方程根的分布情况,推导出模型局部渐近稳定和产生Hopf分岔的时滞临界点。进而利用中心流形方法,计算出确定Hopf分岔性质的显式公式。研究表明,当感染者恢复所需要的时间周期时滞低于临界点时,疾病的传播可以得到有效控制。Considering the importance of innate immunity to individuals in the process of infectious diseases,a delayed SEIS epidemic model with innate immunity and nonlinear cure rate is studied in this paper.Taking the cure period delay of the infectious disease as the bifurcation parameter,the threshold value of the time delay for the local asymptotic stability of the proposed model and occurrence of Hopf bifurcation are obtained by discussing the distribution of the roots of the characteristic equation of the model.Then,by using the central manifold method,the explicit formulas for determining properties of the Hopf bifurcation are calculated.Research shows that the infectious disease can be effectively controlled when the cure period delay of the infectious disease is below the threshold value of the time delay.

关 键 词：先天免疫 非线性治愈率 时滞 SEIS模型 HOPF分岔 

分 类 号：O175[理学—数学]