具Holling-Ⅳ型发生率的SEIAV反应扩散传染病模型的时空动力学分析  

Analysis of Spatio-temporal Dynamics of the SEIAV Response Diffusion Infectious Model with Holling-Ⅳ Incidence

作　　者：张丽娟 丁成东[3] 王福昌 袁静 ZHANG LIJUAN;DING CHENGDONG;WANG FUCHANG;YUAN JING(Department of Basic Courses,Institute of Disaster Prevention,Sanhe 065201,China;Key Laboratory of Earthquake Dynamics of Hebei Province,Institute of Disaster Prevention,Sanhe 065201,China;School of Information Engineering,Institute of Disaster Prevention,Sanhe 065201,China;Beijing Disaster Prevention Science and Technology CO.LTD,Beijing 100081,China)

机构地区：[1]防灾科技学院基础课教学部,三河065201 [2]防灾科技学院河北省地震动力学重点实验室,三河065201 [3]防灾科技学院信息工程学院,三河065201 [4]北京防灾科技有限公司,北京100081

出　　处：《应用数学学报》2024年第5期811-832,共22页Acta Mathematicae Applicatae Sinica

基　　金：防灾科技学院创新创业训练项目(X202411775158);中央高校科研业务专项(ZY20215155)资助。

摘　　要：结合传染病传播过程中的时空扩散效应,考虑Holling-Ⅳ发生率,建立了含有潜伏期、饱和治愈、二次感染、游离病毒的传播及空间扩散等因素的SEIAV传染病模型.得到R_(0)<1时模型的无病平衡点的稳定性以及R_(0)>1时地方病平衡点的持续存在性,并进一步讨论了R_(0)=1时模型无病平衡点全局吸引性.利用算子半群理论证明了模型的适定性,同时还构造了特征值问题,利用主特征值存在的特性给出基本再生数的一般计算方法.最后通过数值模拟,验证了空间扩散的传染病模型传播的影响.The SEIAV infectious disease model containing factors such as incubation period,saturation cure,secondary infection,transmission of free virus was developed by combining the effect of spatial and temporal diffusion and the incidence of Holling-Ⅳ in the process of infectious disease transmission.The stability of the disease-free equilibrium for R_(0)<1 and the persistence of the endemic disease equilibrium point for R_(0)>1 are obtained,and the global attractiveness of the disease-free equilibrium point of the model for R_(0)=1 is further discussed.The fitness of the model is proved using operator semigroup theory,and the eigenvalue problem is also constructed to give a general calculation of the basic regeneration number using the property of the existence of principal eigenvalues.Finally,the effect of spatial diffusion on the spread of the infectious disease model is verified by numerical simulations.

关 键 词：Holling-Ⅳ型发生率 反应扩散模型 基本再生数 阈值动力学 数值模拟 

分 类 号：O29[理学—应用数学]