一类具有脉冲接种的时滞传染病模型稳定性分析  

Analysis of a Delayed Epidemic Model with Pulse Vaccination

作　　者：王来全[1] 夏米西努尔·阿布都热合曼[2] WANG Lai-quan;Xamxinur Abdurahman(Department of Basic Courses,Changji Vocational and Technical College,Changji 831100,China;College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China)

机构地区：[1]昌吉职业技术学院基础教育分院,新疆昌吉831100 [2]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学的实践与认识》2024年第7期141-149,共9页Mathematics in Practice and Theory

基　　金：新疆维吾尔自治区自然科学基金(2022D01A40)。

摘　　要：建立了一类具有脉冲接种的时滞传染病模型,利用庞加莱映射不动点定理和离散动力系统理论得到了模型的无病周期解,当R0<1时,证明了无病周期解的全局吸引性,同时,满足适当条件且ρ>ρ^(*)或τ<τ^(*)或ω>ω^(*)时,我们得到了疾病将消除,并用数值模拟验证了这一结论.最后分析了疾病的持久性。An epidemic model with time delays and pulse vaccination is investigated in this paper.We obtained the infection-free periodic solution of the impulsive epidemic system by using the the discrete dynamical system and the fixed point theory in poincare map.We proved that the globally attractive of the infection-free periodic solution when R0<1.Furthermore,we obtained the disease was faded out under appropriate conditions and the vaccination rate was larger than ρ^(*),or the latent period was larger than>ω^(*),or the time was less than τ^(*),the results are illustrated and corroborated with some numerical experiments.The permanence of the model is investigated analytically.

关 键 词：脉冲接种 无病周期解 全局吸引 持久 

分 类 号：O175[理学—数学] R181[理学—基础数学]