[1]甘文珍,史一欢.一类具扩散的SIRS传染病模型解的渐近性质[J].南京师大学报(自然科学版),2009,32(03):25-30.
　Gan Wenzhen,Shi Yihuan.Asymptotic Properties of Solutions to a SIRS Epidemic Model With Diffusion[J].Journal of Nanjing Normal University(Natural Science Edition),2009,32(03):25-30.
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一类具扩散的SIRS传染病模型解的渐近性质()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第32卷
期数:
2009年03期
页码:
25-30
栏目:
数学
出版日期:
2009-09-30

文章信息/Info

Title:
Asymptotic Properties of Solutions to a SIRS Epidemic Model With Diffusion
作者:
甘文珍1;  史一欢2
1. 江苏技术师范学院数理学院, 江苏常州213001
 2. 南京师范大学生命科学学院, 江苏南京210097
Author(s):
Gan Wenzhen 1; Shi Yihuan 2
1. School of Mathematics and Physics,Jiangsu Teachers University of Technology,Changzhou 213001,China
关键词:
非线性发生率;  暂时免疫力;  时滞;  反应扩散系统;  渐近性质
Keywords:
non linear inc ident ra te;  temporary immunity;  tim e delay;  reaction diffusion system;  asym pto tic properties
分类号:
O175.26
摘要:
研究了一类具有非线性发生率的SIRS传染病模型的弱耦合反应扩散方程组.利用线性化和特征值的方法,讨论了无病平衡点和染病平衡点的局部稳定性,利用Liapunov函数的方法给出了无病平衡点渐近稳定的充分条件.结果表明,在小初值条件下,当接触率小的时候,无病平衡点是渐近稳定的.
Abstract:
The weakly coupled reaction-diffusion system describ ing a SIRS ep idem icm ode lw ith nonlinear inc ident rate is investigated. The loca l asym pto tic stab ilities of equilibr ium s are g iven by lineariza tion and e igenvalue. The asympto tic stabilities o f d isease- free equ ilibrium is investig ated using them e thod of Liapunov functions. Our resu lts show tha t the d isease-free equ ilibrium is asym ptotically stable if the contac t rate is sm a ll and the initial va lues are sm all.

参考文献/References:

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相似文献/References:

[1]方玲玲,齐龙兴.一类SEIRS模型稳定性分析(英文)[J].南京师大学报(自然科学版),2013,36(03):21.
　Fang Lingling,Qi Longxing.The Stability Analysis of an SEIRS Model[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(03):21.

备注/Memo

备注/Memo:
基金项目: 江苏省教育厅自然科学基金( BK2006064 )资助项目.
通讯联系人: 甘文珍, 硕士, 讲师, 研究方向: 偏微分方程. E-m ail:ganw enzhen@ yahoo. com. cn
更新日期/Last Update: 2013-04-23