吉林大学学报（理学版）2025，Vol.63Issue(2)：331-339,9.DOI:10.13413/j.cnki.jdxblxb.2024138
含有疫苗接种项离散传染病模型SIVS的稳定性和分岔分析
Stability and Bifurcation Analysis of Discrete SIVS Epidemic Model with Vaccination Items
摘要
Abstract
Firstly,the basic reproduction number R0 of the SIVS(Susceptible-Infectious-Immune-Susceptible)epidemic model is solved by the method of next generation matrix,through the threshold,the disease-free equilibrium point always exists,and the endemic equilibrium point only exists when R0>1,furthermore,the conditions of extinction and persistence of the disease are determined.Secondly,the stability and the bifurcation situations of the model at the equilibrium point are proved by the properties of Jacobian matrix,Jury criterions and the construction of Lyapunov function.The results show that when R0<1,the disease-free equilibrium point is globally asymptotically stable,and the transcritical bifurcation occurs when R0=1.When R0>1,the endemic equilibrium point is locally asymptotically stable,if the limitation on contact rateβin reality is ignored,the model will produce the period-doubling bifurcation and even chaotic phenomena at the endemic equilibrium point.Finally,numerical simulation and sensitivity index method are used to verify the theoretical analysis results,it is concluded that improving the vaccination rate and recovery rate can effectively reduce the incidence of the disease.关键词
离散模型/模型SIVS/疫苗接种/稳定性/分岔Key words
discrete model/SIVS model/vaccination/stability/bifurcation分类
数学引用本文复制引用
王轲,雷策宇,韩晓玲..含有疫苗接种项离散传染病模型SIVS的稳定性和分岔分析[J].吉林大学学报（理学版）,2025,63(2):331-339,9.基金项目
国家自然科学基金(批准号:12161079)和西北师范大学研究生科研资助项目(批准号:2023KYZZ-S116). （批准号:12161079）
