一类接种率受媒体报道影响的传染病模型分析  

Analysis of a Kind of Epidemic Model with Vaccination Rate Related to Media Coverage

作　　者：王艳妮 刘贤宁[1] WANG Yan-ni;LIU Xian-ning(School of Mathematics and Statistic,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2020年第5期1-6,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671327).

摘　　要：研究了一类接种率受媒体报道影响的SIR传染病模型,同时考虑到媒体报道延迟对模型动力学性态的影响.首先计算了模型的基本再生数R0:R0<1时,利用LaSalle不变集原理得到了无病平衡点的全局稳定性;R0>1时,研究了地方病平衡点的局部稳定性.根据媒体报道是否延迟,分别讨论了以接触率和时滞作为分支参数,系统产生Hopf分支的条件.In this paper, a kind of epidemic model with vaccination rate related to media coverage has been studied, and the influence of media coverage delay on the dynamics of the model been considered. Firstly, the basic reproduction number R0 of the system has been calculated. Then the global stability of disease-free equilibrium been obtained by LaSalle invariant set principle when R0<1, and the local stability of endemic equilibrium been studied when R0>1. According to whether the media coverage is delayed or not, the conditions for Hopf bifurcation have been discussed with contact rate and time delay as bifurcation parameters respectively. Finally, the results have been verified by numerical simulation.

关 键 词：接种 媒体报道 HOPF分支 

分 类 号：O175[理学—数学]