中北大学学报（自然科学版）2024，Vol.45Issue(4)：448-454,7.DOI:10.3969/j.issn.1673-3193.2024.04.005
一类具有标准发生率的SEIR传染病模型的稳定性分析
Stability Analysis of a Class of SEIR Infectious Disease Models with Standard Incidence
摘要
Abstract
According to the transmission mechanism of tuberculosis(TB),a SEIR model of TB infec-tious disease with standard incidence was established,and the stability of the model was discussed.Through constant variation method and the reduction to absurdity,the prove the positive invariant sets of the model is proved;The basic regeneration number R0 of the model is calculated by the next generation matrix method,and it is proved that the disease-free equilibrium point D0 is globally asymptotically stable by constructing Lyapunov function method when R0≤1.It is proved by Hurwitz criterion that the endemic equilibrium point D* is locally asymptotically stable when R0>1,and based on the Li-Mulowney geometric approach to determine the global stability,we obtain the conditions for global stability of the endemic equilibrium.Finally,the validity of the results is verified by numerical simulation.关键词
肺结核/SEIR传染病模型/Hurwitz判据/Li-Mulowney几何方法/稳定性Key words
TB/SEIR infectious disease model/Hurwitz criterion/Li-Mulowney geometric method/stability分类
数理科学引用本文复制引用
宫红艳,薛亚奎..一类具有标准发生率的SEIR传染病模型的稳定性分析[J].中北大学学报（自然科学版）,2024,45(4):448-454,7.基金项目
国家自然科学基金资助项目(11971278) （11971278）
山西省自然科学青年基金资助项目(201801D221040) （201801D221040）
