在禽类与人之间传播的禽流感反应扩散模型  

An Avian-human Influenza Model with Reaction Diffusion

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,西安710048

出　　处：《湖北民族大学学报（自然科学版）》2024年第2期276-284,共9页Journal of Hubei Minzu University:Natural Science Edition

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

摘　　要：为了研究禽类和人的流动性对禽流感传播的影响,考虑禽和人的流动性,建立了一个禽流感在禽与人之间传播的反应扩散模型。首先证明了模型解的全局存在性,其次利用下一代算子的谱半径方法计算了模型的基本再生数,并分析了模型的阈值动力学,证明了无病稳态的稳定性、疾病的持久性以及正稳态的存在性。最后通过数值模拟,验证了模型的理论结果。结果表明,对染病禽类进行隔离,从而降低禽与人的接触率可有效控制禽流感的传播。In order to study the impact of the mobility of birds and humans on the spread of avian influenza,this article considered the mobility of birds and humans and established a reaction-diffusion model to study the propagation dynamics of avian influenza between humans and birds.Firstly,the global existence of the model solution was proved.Secondly,the basic reproduction number of the model was calculated using the spectral radius method of the next generation operator,and the threshold dynamics of the model were analyzed.The stability of disease-free steady state,the persistence of the disease and the existence of the positive steady state were proved.Finally,the theoretical results were verified through numerical simulations.The results indicate that isolating infected birds and reducing the contact rate between birds and humans can effectively control the spread of avian influenza.

关 键 词：禽流感 反应扩散 全局渐近稳定性 基本再生数 持久性 正稳态 

分 类 号：O175.1[理学—数学]