# [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] 点击复制 社会经济领域中一类扩散现象的数学模型() 分享到： var jiathis_config = { data_track_clickback: true };

32

2002年第4期

668-671

2002-07-20

## 文章信息/Info

Title:
Mathematical model of a diffusion phenomenon in social-economic region

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):
1 Department of Applied Mathematics, Southeast University, Nanjing 210096, China
2 Institute of Management Science and Engineering, Nanjing University, Nanjing 210093, China

Keywords:

N94
DOI:
10.3969/j.issn.1001-0505.2002.04.030

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.