斑块环境下具有脉冲效应的SIQR传染病模型的动力学分析  

Dynamical Analysis of the SIQR Epidemic Model with Impulse Effects in a Patchy Environment

作　　者：张悦 杨志春 ZHANG Yue;YANG Zhichun(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《应用数学》2025年第2期574-583,共10页Mathematica Applicata

基　　金：国家自然科学基金(11971081,10471061);重庆市教育委员会科学技术研究项目(KJZDM202000502);重庆市教委雏鹰计划研究项目(CY220503);重庆市研究生科研创新项目(CYS23414)。

摘　　要：斑块效应和脉冲控制策略对传染病的传播具有重要影响,基于此提出了一个斑块环境下具有脉冲疫苗接种和脉冲境外输入的SIQR传染病模型.首先,证明了系统的解的有界性和疾病消失时正周期解的唯一性.其次,利用Floquet定理、脉冲比较原理、线性化方法和基解矩阵谱理论的性质,获得了系统的动力学阈值R_(0),证明了当R_(0)<1时,系统的无病周期解是全局渐近稳定的.最后,利用庞加莱映射、不可约矩阵的性质和持久性理论等方法,证明了当R_(0)>1时,系统是一致持久的.Patch effects and impulse control strategies have an important impact on the spread of infectious diseases,based on which a SIQR epidemic model with pulse vaccination and pulse abroad input in a patch environment is proposed.First,the boundedness of the solutions of the system and the uniqueness of the positive periodic solution when the disease disappears are proved.Second,using Floquet’s theorem,the impulse comparison principle,the linearization method and the properties of the spectral theory of the basis solution matrix,the dynamical threshold R_(0)of the system is obtained.It is proved that the disease-free periodic solution of the system is globally asymptotically stable when R_(0)<1.Finally,it is shown that the system is uniformly persistent when R_(0)>1,using methods such as the Poincar´e mapping,the properties of irreducible matrices and persistence theory.

关 键 词：斑块环境 SIQR传染病模型 脉冲疫苗接种 脉冲境外输入 稳定性 持久性 

分 类 号：O175.13[理学—数学]