具有媒体报道和个人防护意识的多时滞媒介传染病模型Hopf分支分析  

Media Coverage and Personal Protection Awareness with Hopf Bifurcation Analysis of Multi-Time Delay Vector-Borne Disease Model

作　　者：郝新杰 聂麟飞[1] HAO Xinjie;NIE Linfei(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《新疆大学学报（自然科学版中英文）》2024年第4期408-418,共11页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金“多宿主传染病模型动力学分析及应用”(11961066);新疆维吾尔自治区自然科学基金“环境异质与种群异质的传染病的建模与防控策略分析”(2021D01E12).

摘　　要：考虑到媒体报道、个人防护意识和时滞效应对媒介传染病传播与防控的影响,建立一类具有媒体报道延迟和潜伏期时滞影响的媒介传染病模型.首先,给出基本再生数的精确表达式,并用其刻画平衡态的存在性与稳定性,以及Hopf分支的存在性.即,当基本再生数小于1时,媒体报道延迟和病原体在媒介体内的潜伏期时滞不会影响模型无病平衡点的稳定性,而当基本再生数大于1时,媒体报道的延迟会影响地方病平衡点的稳定性,模型会产生Hopf分支.进一步,通过使用分支定理讨论Hopf分支的方向并得到周期解稳定性的充分条件.最后,通过一些数值算例解释主要的理论结果.Considering the effects of media coverage,personal protection awareness and time delays on the spread of vector-borne diseases,a model of vector-borne diseases with delayed media coverage and incubation period delays is developed.Firstly,the exact expression of the basic reproduction number is given and used to characterize the existence and stability of the equilibria and the existence of the Hopf bifurcation.That is,when the basic reproduction number is less than 1,the stability of disease-free equilibrium will not be affected by the media coverage delay and the latency delay of virus in vectors.When the basic reproduction number is greater than 1,the media coverage delay will affect the stability of the endemic equilibrium,and the model will generate the Hopf bifurcation.Further,by using the bifurcation theorem,the direction of Hopf bifurcation is discussed and some sufficient conditions for the stability of periodic solution are obtained.Finally,some numerical examples are given to explain the main theoretical results.

关 键 词：媒介传染病 媒体报道 基本再生数 Hopf分支与稳定性 

分 类 号：O175[理学—数学]