| 郭宇,朱惠延,贺芳芳.具Holling-III型治疗函数的SEIR模型及其稳定性分析[J].南华大学学报(自然科学版),2021,(5):80~85.[GUO Yu,ZHU Huiyan,HE Fangfang.Stability Analysis of a SEIR Model with Holling-III Therapeutic Function[J].Journal of University of South China(Science and Technology),2021,(5):80~85.] |
| 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 |
| 投稿时间：2021-04-21 |
| DOI： |
| 中文关键词: 治疗函数 SEIR传染病模型 局部渐近稳定性 数值模拟 |
| 英文关键词:treatment function SEIR epidemic model locally asymptotic stability numerical simulation |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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. |
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