| 具Holling-III型治疗函数的SEIR模型及其稳定性分析 |
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| 引用本文： | 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. |
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| 作者姓名： | 郭宇 朱惠延 贺芳芳 |
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| 作者单位： | 南华大学 数理学院,湖南 衡阳 421001 |
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| 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。
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| 关 键 词： | 治疗函数 SEIR传染病模型 局部渐近稳定性 数值模拟 |
| 收稿时间： | 2021/4/21 0:00:00 |
Stability Analysis of a SEIR Model with Holling-III Therapeutic Function |
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| GUO Yu,ZHU Huiyan,HE Fangfang.Stability Analysis of a SEIR Model with Holling-III Therapeutic Function[J].Journal of Nanhua University:Science and Technology,2021(5):80-85. |
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| Authors: | GUO Yu ZHU Huiyan HE Fangfang |
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| Institution: | School of Mathmatics and Physics, University of South China, Hengyang, Hunan 421001, China |
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| Abstract: | 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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| Keywords: | treatment function SEIR epidemic model locally asymptotic stability numerical simulation |
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