引用本文:马艳丽, 聂东明, 于萍.具有非单调传染率与连续干扰的SIQR模型的稳定性研究(J/M/D/N,J:杂志,M:书,D:论文,N:报纸).期刊名称,2021,38(2):48-55
CHEN X. Adap tive slidingmode contr ol for discrete2ti me multi2inputmulti2 out put systems[ J ]. Aut omatica, 2006, 42(6): 4272-435
【打印本页】   【下载PDF全文】   查看/发表评论  【EndNote】   【RefMan】   【BibTex】
←前一篇|后一篇→ 过刊浏览    高级检索
本文已被:浏览 723次   下载 1683 本文二维码信息
码上扫一扫!
分享到: 微信 更多
具有非单调传染率与连续干扰的SIQR模型的稳定性研究
马艳丽, 聂东明, 于萍
安徽新华学院 通识教育部,合肥 230088
摘要:
将连续方式的接种、剔除和隔离干扰引入模型,建立了一类具有非单调传染率的SIQR传染病模型;首先,通过计算得到了疾病流行的阈值R0及无病平衡点和地方病平衡点存在的条件;其次,当R0<1时,采用Routh Hurwitz判据和极限方程理论证明了无病平衡点具有全局渐近稳定性,当R0>1时,运用Liapunov函数和LaSalle不变集原理证明了地方病平衡点E*也具有全局渐近稳定性;接着,为了进一步说明理论研究的正确性,利用Matlab软件进行了计算机模拟;最后,借助阈值R0的偏导数,对连续方式的接种、剔除和隔离策略进行了比较和分析。
关键词:  基本再生数  平衡点  稳定性  非单调传染率
DOI:
分类号:
基金项目:
Stability Research of a SIQR Model with Nonmonotone Infection Rate and Continuous Perturbations
MA Yan-li,NIE Dong-ming,YU Ping
Department of Common Courses,Anhui Xinhua University,Hefei 230088,China
Abstract:
Continuous vaccination,elimination and quarantine perturbations are introduced,and a SIQR epidemic model with nonmonotone infection rate is established.Firstly,the threshold R0 which determines whether the disease is extinct or not and the conditions for the existence of equilibriums are obtained by the calculation.Secondly,the globally asymptotical stability of the disease free equilibrium E0 is proved when R0<1 by means of Routh Hurwitz criterion and limit equation theory.By Liapunov function and LaSalle invariance principle,the globally asymptotical stability of the unique endemic equilibrium E* is also proved when R0>1.Thirdly,computer simulation is carried out to illustrate the correctness of the theoretical research by Matlab software.Finally,the continuous vaccination,elimination and quarantine strategies are compared and analyzed with the partial derivative of the threshold R0.
Key words:  basic reproductive number  equilibrium point  stability  nonmonotone infection rate
系统正在查找本文的参考文献,请稍候...
系统正在查找本文的被引信息,请稍候...
系统正在获取相似文献,请稍候...
重庆工商大学学报(自然科学版) 版权所有
地址:中国 重庆市 南岸区学府大道19号 重庆工商大学学术期刊社 邮编:400067
电话:023-62769495 传真:
您是第4555799位访客
关注微信二维码