[1]韩瑞珠,盛昭瀚.社会经济领域中一类扩散现象的数学模型[J].东南大学学报(自然科学版),2002,32(4):668-671.[doi:10.3969/j.issn.1001-0505.2002.04.030]
 Han Ruizhu,Sheng Zhaohan.Mathematical model of a diffusion phenomenon in social-economic region[J].Journal of Southeast University (Natural Science Edition),2002,32(4):668-671.[doi:10.3969/j.issn.1001-0505.2002.04.030]
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社会经济领域中一类扩散现象的数学模型()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
32
期数:
2002年第4期
页码:
668-671
栏目:
经济与管理
出版日期:
2002-07-20

文章信息/Info

Title:
Mathematical model of a diffusion phenomenon in social-economic region
作者:
韩瑞珠1盛昭瀚2
1 东南大学应用数学系,南京 210096; 2 南京大学管理科学与工程研究院,南京 210093
Author(s):
Han Ruizhu1 Sheng Zhaohan2
1 Department of Applied Mathematics, Southeast University, Nanjing 210096, China
2 Institute of Management Science and Engineering, Nanjing University, Nanjing 210093, China
关键词:
扩散现象 社会经济领域 数学模型
Keywords:
diffusion phenomenon social and economic region mathematical model
分类号:
N94
DOI:
10.3969/j.issn.1001-0505.2002.04.030
摘要:
利用数学模型讨论社会经济现象中两类群体在互动中的扩散现象规律,指出这种现象是否保持取决于内增长率.当内增长率小于零时,扩散现象消除的平衡点总存在,并且这个平衡点全局渐近稳定,从而扩散现象逐渐消失. 当内增长率大于零时,这个平衡点变得不稳定.但保持扩散现象的平衡点存在惟一.在平衡点,当两类群体人数相等时, 它们的接触率与感染率相同. 由此推出当内增长率大于零时,扩散现象保持,且在一定条件下有惟一的吸引子.
Abstract:
A diffusion phenomenon in the interaction of two communities is discussed through mathematical methods and it is pointed out that the kind of phenomenon is decided by the intrinsic growth rate. When the intrinsic growth rate is less than zero, the disease free equilibrium of the model exists, and it is global asymptotic stable. So the kind of phenomenon disappears gradually. When the intrinsic growth rate is larger than zero, the disease free equilibrium of the model is not stable, and an only epidemic equilibrium of the model exists. At the equilibrium point, the contact rate is equal to the infection rate when the number of two communities are equal. Thus the kind of phenomenon keeps and there is a unique attractor under certain condition.

参考文献/References:

[1] Robert B Banks. Growth and diffusion phenomena[M].New York:Springer-Verlag,1994.126.
[2] 理查德·斯通.社会科学中的数学和其他论文[M].楼克明等译.北京:首都经济贸易大学出版社,2000.173-176.
[3] Doyle M,Greenhalgh D.Asymmetry and multiple endemic equilibria in a model for HIV transmission in a heterosexual population[J]. Mathematical and Computer Modelling,1999,29:43-61.
[4] Brauer F,van den Driessche P.Models for transmission of disease with immigration of infectives[J].Mathematical Biosciences,2001,171:143-154.
[5] Murray J D.Mathematical biology[M].New York:Springer-Verlag,1993.629.

备注/Memo

备注/Memo:
基金项目: 国家自然科学基金资助项目(69874004,19971013)、江苏省自然科学基金资助项目(BK99001).
作者简介: 韩瑞珠(1959—),女,博士生,副教授.
更新日期/Last Update: 2002-07-20