一类传染病模型的Turing失稳研究

宋礼; 靳祯; 孙桂全

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一类传染病模型的Turing失稳研究

应用基础研究 | 更新时间：2026-09-14

- 一类传染病模型的Turing失稳研究
- Turing Instability in an Epidemic Model
- 中北大学学报（自然科学版） 2011年32卷第6期页码：666-670
- 作者机构：
  
  中北大学理学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金资助项目(60771026);新世纪优秀人才支持计划资助项目(NCET050271);山西省自然科学基金资助项目(2006011009)
- DOI：
  中图分类号：
- 纸质出版：2011
- 稿件说明：
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宋礼, 靳祯, 孙桂全. 一类传染病模型的Turing失稳研究[J]. 中北大学学报（自然科学版）, 2011,32(6):666-670.

宋礼, 靳祯, 孙桂全. Turing Instability in an Epidemic Model[J]. 2011, 32(6): 666-670.
宋礼, 靳祯, 孙桂全. 一类传染病模型的Turing失稳研究[J]. 中北大学学报（自然科学版）, 2011,32(6):666-670. DOI：

宋礼, 靳祯, 孙桂全. Turing Instability in an Epidemic Model[J]. 2011, 32(6): 666-670. DOI：

摘要

为了很好地控制传染病在人类的传播

研究了一类具有非线性传染率βS1/2I1/2的空间传染病模型的Turing失稳.通过对ODE模型进行了详细的Hopf分支分析

算出第一Lyapunov系数

得到此Hopf分支是亚临界分支.对于空间模型

给出了精确Turing失稳的参数条件

并给出了相应的数值模拟

得到了条状和点状共存的斑图.理论分析和数值模拟表明

利用反应扩散方程建模是揭示空间动力学复杂性机理的一个有效工具

也为控制疾病的传播提供了有力的理论依据.

Abstract

For the effective control of the disease

a spatial epidemic model with nonlinear incidence rate βS1/2I1/2 was investigated.A detailed Hopf bifurcation analysis to the ODE model was performed and the direction of the subcritical Hopf bifurcation and the first Lyapunov index were derived.For the spatial model

the precise conditions of Turing instability were given.Both the results of theoretic analysis and numerical simulations reveal the efficiency of the above work in investigating the spatial dynamics in the actual world

which may provide guidance to disease controlling.

关键词

Keywords

references

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马知恩,靳祯.总人口在变化的流行病动力学模型[J].华北工学院学报,2001,22(4):262-271.Ma Zhien,Jin Zhen.Dynamic models of infectious diseases in a population with varying size[J].Journal of NorthChina Institute of Technology,2001,22(4):262-271.(in Chinese)

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Sun G,Jin Z,Liu Q X,Li L.Pattern formation in a spatial S-I model with non-linear incidence rates[J].Journal ofStatistical Mechanics:Theory and Experiment,2007(11):11011.

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