具有阶段结构的SEI传染病模型的全局分析

杜燕飞,肖鹏,曹慧

doi:10.13718/j.cnki.xsxb.2018.09.002

西南师范大学学报(自然科学版)

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具有阶段结构的SEI传染病模型的全局分析

杜燕飞,肖鹏,曹慧. 具有阶段结构的SEI传染病模型的全局分析[J]. 西南师范大学学报(自然科学版), 2018, 43(9): 6-10. doi: 10.13718/j.cnki.xsxb.2018.09.002

引用本文:

杜燕飞,肖鹏,曹慧. 具有阶段结构的SEI传染病模型的全局分析[J]. 西南师范大学学报(自然科学版), 2018, 43(9): 6-10. doi: 10.13718/j.cnki.xsxb.2018.09.002

DU Yan-fei, XIAO Peng, CAO Hui. On Dynamic Behavior of an SEI Epidemic Model with Stage-Structure[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(9): 6-10. doi: 10.13718/j.cnki.xsxb.2018.09.002

Citation:

DU Yan-fei, XIAO Peng, CAO Hui. On Dynamic Behavior of an SEI Epidemic Model with Stage-Structure[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(9): 6-10. doi: 10.13718/j.cnki.xsxb.2018.09.002

具有阶段结构的SEI传染病模型的全局分析

杜燕飞,肖鹏,曹慧

陕西科技大学数学系, 西安 710021

On Dynamic Behavior of an SEI Epidemic Model with Stage-Structure

DU Yan-fei, XIAO Peng, CAO Hui

Department of Mathematics, Shaanxi University of Science and Technology, Xi'an 710021, China

摘要: 建立和研究了一类具有幼年和成年两个阶段结构的SEI传染病模型，通过分析平衡点的特征方程，讨论了平衡点的局部稳定性.得到了基本再生数是传染病最终消除或成为地方病的阀值，当基本再生数小于1时，无病平衡点为全局稳定的，传染病最终消除，否则系统将一致持续生存.
- SEI传染病模型 /
- 阶段结构 /
- 稳定性 /
- 基本再生数
Abstract: In this paper, an SEI Epidemic Model with Stage-structure is established and studied, in which the population is divided into two stages:immature stage and mature stage. By discussing the eigenvalue equation of the equilibriums, locally asymptotic stability of the equilibriums are obtained. It is shown that the global dynamics is determined by the basic reproduction number, when the basic reproduction number is less than 1, the disease free equilibrium is globally asymptotically stable; otherwise the disease persists.
- SEI epidemic model /
- stage-structured /
- stability /
- the basic reproduction number .

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