人-环境-家禽之间禽流感传播模型的稳定性分析  

Stability Analysis of Avian Influenza Transmission Model Between Human,Environment and Poultry

作　　者：田苗苗 刘俊利[1] TIAN Miaomiao;LIU Junli(School of Science,Xi'an Polytechnic University,Xi'an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《沈阳大学学报（自然科学版）》2023年第6期544-550,共7页Journal of Shenyang University：Natural Science

基　　金：国家自然科学基金资助项目(11801431);陕西省自然科学基础研究计划项目(2021JM-445)。

摘　　要：为了研究禽流感在人、家禽以及环境中的传播动态,建立了一个SI-V-SIR传染病模型。利用微分方程基本定理证明了模型解的有界性和非负性。给出了模型的基本再生数R_(0),并分析了模型的阈值动力学:当R_(0)<1时,无病平衡点E_(0)全局渐近稳定;当R_(0)>1时,地方病平衡点E*存在,且是局部渐近稳定的。当家禽因病死亡率可以忽略时,证明了地方病平衡点的全局渐近稳定性。通过对模型进行数值分析,研究了控制禽流感传播的有效措施。In order to study the transmission dynamics of avian influenza in humans,poultry and the environment,an SI-V-SIR infectious disease model was established.Firstly,the boundedness and nonnegativity of the solution of the model were proved using the basic theorems of differential equations.Secondly,the basic reproduction number R_(0)of the model was given,and the threshold dynamics of the model were analyzed:if R_(0)<1,the disease-free equilibrium E_(0)was globally asymptotically stable;if R_(0)>1,the endemic equilibrium E*existed and was locally asymptotically stable.The global asymptotic stability of the endemic equilibrium was proved when the disease-induced death rate of domestic poultry could be ignored.Numerical analyses of the model were carried out to explore effective control measures for the spread of avian influenza.

关 键 词：禽流感 SI-V-SIR传染病模型 全局渐近稳定性 基本再生数 偏秩相关系数 

分 类 号：O175.1[理学—数学]