一类受媒体报道滞后性影响的传染病模型  

An Epidemic Model Affected by Delayed Media Coverage

作　　者：阳丽君 班相函 王文龙[1] YANG Lijun;BAN Xianghan;WANG Wenlong(College of Science,Northeast Forestry University,Harbin 150006,China)

机构地区：[1]东北林业大学理学院,黑龙江哈尔滨150006

出　　处：《湖北民族大学学报（自然科学版）》2022年第4期420-424,450,共6页Journal of Hubei Minzu University:Natural Science Edition

基　　金：中央高校基本科研业务费专项资金资助项目(2572022DJ04).

摘　　要：针对媒体信息对传染病的影响问题,考虑媒体报道的滞后因素,提出了一类具有媒体报道滞后效应的传染病模型.首先,定义了模型的基本再生数,分析了模型的无病平衡点和地方病平衡点的局部稳定性.其次,给出系统存在纯虚根以及产生Hopf分支的条件.最后,通过数值模拟验证结果.研究表明,媒体报道产生的时滞会引发Hopf分支、产生周期解、破坏系统的稳定性,说明媒体对传染病的延迟报道不利于传染病的预测和防治.Aiming at the influence of media information on epidemic diseases,considering the delayed factor of media reports,a kind of epidemic disease model with time-delay of media coverage is proposed.Firstly,the basic regeneration number of the model is defined,and the stability of disease-free equilibrium and local equilibrium of the model is analyzed.Secondly,the existence of pure imaginary roots and the conditions of Hopf bifurcation are given.Finally,the results are verified by numerical simulation.The results show that the time-delay of media reports can trigger Hopf branching,produce periodic solutions,and destroy the stability of the system,which indicates that the delayed media reports on epidemic diseases are not conducive to the prediction and treatment of diseases.

关 键 词：媒体报道 传染病模型 时滞 HOPF分支 稳定性 平衡点 

分 类 号：O175[理学—数学]