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基于白噪声的网络传染病模型动力学分析

曹晓春 荆文君 靳祯

曹晓春,荆文君,靳祯. 基于白噪声的网络传染病模型动力学分析 [J]. 应用数学和力学,2022,43(6):1-10 doi: 10.21656/1000-0887.430009
引用本文: 曹晓春,荆文君,靳祯. 基于白噪声的网络传染病模型动力学分析 [J]. 应用数学和力学,2022,43(6):1-10 doi: 10.21656/1000-0887.430009
Xiaochun CAO, Wenjun JING, Zhen JIN. Dynamic Analysis of Network Epidemic Model Based on the White Noise[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.430009
Citation: Xiaochun CAO, Wenjun JING, Zhen JIN. Dynamic Analysis of Network Epidemic Model Based on the White Noise[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.430009

基于白噪声的网络传染病模型动力学分析

doi: 10.21656/1000-0887.430009
基金项目: 国家自然科学基金(12101373;61873154);山西省高等学校科技创新项目(2020L0246);山西省基础研究项目(20210302124261);山西省自然科学基金(201901D211411)
详细信息
    作者简介:

    曹晓春(1980—),女,博士(E-mail:caoxc@sxufe.edu.cn)

    荆文君(1990—),女,博士(E-mail:jingwj@sxufe.edu.cn)

    靳祯(1965—),男,博士(通讯作者. E-mail:jinzhn@263.net)

  • 中图分类号: O193

Dynamic Analysis of Network Epidemic Model Based on the White Noise

  • 摘要: 该文基于确定性网络传染病模型, 建立了白噪声影响下的随机网络传染病模型, 证明了模型全局解的存在唯一性, 利用随机微分方程理论得到了传染病随机灭绝和随机持久的充分条件。结果表明, 白噪声对网络传染病传播动力学有很大的影响, 白噪声能有效抑制传染病的传播, 大的白噪声甚至能让原本持久的传染病变得灭绝。最后, 通过数值模拟验证了理论结果。
  • 图  1  不同初值下,确定性模型(1)灭绝情形与随机性模型(2)灭绝情形的I(t)路径模拟:(a) 初值Ik(0)=0.5;(b) 初值Ik(0)=0.8

    Figure  1.  I(t) path simulation on different values with extinction case of deterministic model (1) and extinction case of stochastic model (2): (a) initial value Ik(0)=0.5;(b) initial value Ik(0)=0.8

    图  2  确定性模型(1)灭绝(持久)情形与随机性模型(2)灭绝情形的I(t)路径模拟:(a) 确定性模型(1)灭绝情形与随机性模型(2)灭绝情形;(b) 确定性模型(1)持久情形与随机性模型(2)灭绝情形

    Figure  2.  I(t) path simulation with extinction (persistence) case of deterministic model (1) and extinction case of stochastic model (2): (a) extinction case of deterministic model (1) and extinction case of stochastic model (2); (b) persistence case of deterministic model (1) and extinction case of stochastic model (2)

    图  3  不同初值下,确定性模型(1)持久情形与随机性模型(2)持久情形的I(t)路径模拟:(a) 初值Ik(0)=0.5;(b) 初值Ik(0)=0.8

    Figure  3.  I(t) path simulation on different values with persistence case of deterministic model (1) and persistence case of stochastic model (2): (a) initial value Ik(0)=0.5;(b) initial value Ik(0)=0.8

    图  4  不同初值下,确定性模型(1)与随机性模型(2)的I(t)路径模拟图:(a) 初值Ik(0)=0.01;(b) 初值Ik(0)=0.1

    Figure  4.  I(t) path simulation on different values with deterministic model (1) and stochastic model (2): (a) initial value Ik(0)=0.01; (b) initial value Ik(0)=0.1

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出版历程
  • 收稿日期:  2022-01-14
  • 修回日期:  2022-03-11
  • 网络出版日期:  2022-05-12

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