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Local Stability and Global Stability of SIQS Models for Disease
Author(s): CHEN Junjie
Pages: 57-
64
Year: 2004
Issue:
1
Journal: JOURNAL OF BIOMATHEMATICS
Keyword: 传染病; 隔离; 传染病平衡点; 全局稳定性;
Abstract: 首先建立了一类具常恢复率,有效接触率依赖于总人数的SIQS传染病模型,并得到了闽值参数σ的表达式.如果σ≤ 1,则疾病消除平衡点全局稳定;如果σ>1,则存在唯一的传染病平衡点且是局部渐近稳定的.对于带有双线性传染率和标准传染率的两个相应模型,我们进一步证明了当σ>1时传染病平衡点的全局稳定性.其次对于带隔离项修正的传染率的相应模型,我们同样证明了传染病平衡点只要存在唯一就一定全局稳定的结论.上述结果均推广和改进了Hethcote et al.(2002)的相应工作.
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