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

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

曹晓春^1,,
荆文君^2,,
靳祯^3, ,

1.
山西财经大学应用数学学院，太原 030006
2.
山西财经大学统计学院，太原 030006
3.
山西大学复杂系统研究所，太原 030006

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
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- 被引次数: 0
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
- 刊出日期: 2022-06-30

Dynamic Analysis of the Network Epidemic Model Based on White Noise

CAO Xiaochun^1
,,
JING Wenjun^2
,,
JIN Zhen^{3
, ,}

1.
School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, P.R.China
2.
School of Statistics, Shanxi University of Finance and Economics, Taiyuan 030006, P.R.China
3.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, P.R.China

摘要

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。
- 传染病模型 /
- 网络 /
- 白噪声
Abstract:
Based on the deterministic network infectious disease model, a stochastic network infectious disease model under the influence of white noise was established, and the existence and uniqueness of the global solution to the model were proved. With the theory of stochastic differential equations, sufficient conditions for stochastic extinction and persistence of infectious diseases were obtained. The results show that, white noise has a great impact on the transmission dynamics of network infectious diseases. White noise can effectively suppress the spread of infectious diseases, and large white noise can even make the original persistent infectious diseases become extinct. Finally, the theoretical results were verified through numerical simulations.
- epidemic model /
- network /
- white noise

HTML全文

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I_k(0)=0.5；(b) 初值I_k(0)=0.8

Figure 1. For different initial values, I(t) path simulations of the extinction case of deterministic model (1) and the extinction case of stochastic model (2): (a) initial value I_k(0)=0.5；(b) initial value I_k(0)=0.8

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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 simulations of the extinction (persistence) case of deterministic model (1) and the extinction case of stochastic model (2): (a) the extinction case of deterministic model (1) and the extinction case of stochastic model (2); (b) the persistence case of deterministic model (1) and the extinction case of stochastic model (2)

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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I_k(0)=0.5；(b) 初值I_k(0)=0.8

Figure 3. For different initial values, I(t) path simulations of the persistence case of deterministic model (1) and the persistence case of stochastic model (2): (a) initial value I_k(0)=0.5；(b) initial value I_k(0)=0.8

下载: 全尺寸图片幻灯片

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I_k(0)=0.01；(b) 初值I_k(0)=0.1

Figure 4. For different initial values, I(t) path simulations of deterministic model (1) and stochastic model (2): (a) initial value I_k(0)=0.01; (b) initial value I_k(0)=0.1

下载: 全尺寸图片幻灯片

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