具Holling-III型治疗函数的SEIR模型及其稳定性分析  

Stability Analysis of a SEIR Model with Holling-III Therapeutic Function

作　　者：郭宇 朱惠延[1] 贺芳芳 GUO Yu;ZHU Huiyan;HE Fangfang(School of Mathmatics and Physics, University of South China, Hengyang, Hunan 421001, China)

机构地区：[1]南华大学数理学院,湖南衡阳421001

出　　处：《南华大学学报（自然科学版）》2021年第5期80-85,共6页Journal of University of South China：Science and Technology

摘　　要：利用常微分方程定性与稳定性分析理论研究了一类具Holling-III型治疗函数的SEIR传染病模型,给出了基本再生数的定义,分析了模型的正定性,有界性以及无病平衡点的局部渐近稳定性,并判断了地方病平衡点局部渐近稳定需满足的条件。最后通过数值模拟验证了理论分析结果。Using the theory of ordinary differential equation qualitative and stability analysis to study SEIR epidemic model with Holling-III treatment function,the definition of the basic reproductive number is given,the positive definiteness,boundedness and the locally asymptotic stability of the disease-free equilibrium of the model are analyzed,and the locally asymptotically stable endemic equilibrium conditions to be fulfilled are presented.Finally,the results of theoretical analysis are verified by numerical simulation.

关 键 词：治疗函数 SEIR传染病模型 局部渐近稳定性 数值模拟 

分 类 号：O175[理学—数学]