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具有年龄结构和水平传播的媒介传染病模型研究

梁霜霜 聂麟飞 胡琳

梁霜霜, 聂麟飞, 胡琳. 具有年龄结构和水平传播的媒介传染病模型研究[J]. 华东师范大学学报(自然科学版), 2021, (3): 47-55. doi: 10.3969/j.issn.1000-5641.2021.03.006
引用本文: 梁霜霜, 聂麟飞, 胡琳. 具有年龄结构和水平传播的媒介传染病模型研究[J]. 华东师范大学学报(自然科学版), 2021, (3): 47-55. doi: 10.3969/j.issn.1000-5641.2021.03.006
LIANG Shuangshuang, NIE Linfei, HU Lin. Analysis of vector-borne infectious disease model with age-structured and horizontal transmission[J]. Journal of East China Normal University (Natural Sciences), 2021, (3): 47-55. doi: 10.3969/j.issn.1000-5641.2021.03.006
Citation: LIANG Shuangshuang, NIE Linfei, HU Lin. Analysis of vector-borne infectious disease model with age-structured and horizontal transmission[J]. Journal of East China Normal University (Natural Sciences), 2021, (3): 47-55. doi: 10.3969/j.issn.1000-5641.2021.03.006

具有年龄结构和水平传播的媒介传染病模型研究

doi: 10.3969/j.issn.1000-5641.2021.03.006
基金项目: 国家自然科学基金(1961066, 11771373); 新疆维吾尔自治区高校科研计划(XJEDU2018I001)
详细信息
    通讯作者:

    聂麟飞, 男, 教授, 研究方向为微分方程及其应用. E-mail: lfnie@163.com

  • 中图分类号: O175

Analysis of vector-borne infectious disease model with age-structured and horizontal transmission

  • 摘要: 考虑到病毒变异和感染年龄的普遍存在性, 提出了一类具有潜伏年龄和水平传播的媒介-宿主传染病模型, 给出了基本再生数${\cal R}_0$的精确表达式, 刻画了该模型无病平衡态和地方病平衡态的存在性. 进一步, 利用线性近似方法和构造合适的Lyapunov函数及LaSalle不变原理等方法, 证明了当${\cal R}_0<1$时, 无病平衡态${\cal E}_{0}$是全局渐近稳定的, 疾病也最终趋于灭绝; 而当${\cal R}_0>1$时, 地方病平衡态是全局渐近稳定的, 疾病将持续下去而形成地方病.
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出版历程
  • 收稿日期:  2020-01-19
  • 刊出日期:  2021-05-01

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