具有接种的SV_(1)V_(2)IR传染病模型的定性分析  

Global Stability of An SV_(1) V_(2) IR Epidemic Model with Vaccination

作　　者：孙丹丹 马丽[1] 何琪安 周迅 周玲[1] Sun Dandan;Ma Li;He Qi’an;Zhou Xun;Zhou Ling(College of Mathematics and Science,Xinjiang Agricultural University,Urumqi 830052,China)

机构地区：[1]新疆农业大学数理学院,新疆乌鲁木齐830052

出　　处：《宁夏大学学报（自然科学版）》2022年第1期12-16,共5页Journal of Ningxia University(Natural Science Edition)

基　　金：新疆维吾尔自治区高校科研计划资助项目(XJEDU2018Y021);新疆农业大学大学生创新创业训练计划项目(dxscx2021406)。

摘　　要：构建了一类具有接种的SV_(1)V_(2)IR传染病模型.首先,求得模型的平衡点,并应用基本再生矩阵的方法,得到模型的基本再生数.其次,使用线性化、Hurwitz判据和构造适当的Lyapunov函数等方法,证明了当R_(0)<1时无病平衡点全局渐近稳定;当R_(0)>1时无病平衡点不稳定,而地方病平衡点全局渐近稳定.最后,用偏置相关系数(PRCC)的方法做了相应的数值模拟.A kind of SV_(1)V_(2)IR infectious disease model with vaccination is established.Firstly,the equilibrium of the model and the basic reproduction number by using the basic regeneration matrix is derived.Secondly,the globally asymptotically stable of the disease-free equilibrium when R_(0)<1,when R_(0)>1 the disease-free equilibrium is unstable and the endemic equilibrium is globally asymptotically stable by using the linearization,Hurwitz criterion and constructing Lyapunov functions is obtained.Finally,the corresponding numerical simulation is carried out by using partial rank correlation coefficients(PRCC),and a practical basis for the theory is provided.

关 键 词：传染病模型 稳定性 基本再生数 偏置相关系数 

分 类 号：O175[理学—数学] O231.3[理学—基础数学]