| 一类具有饱和发生率和治疗的SEIR模型 |
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| 引用本文： | 刘国永,李桂花. 一类具有饱和发生率和治疗的SEIR模型[J]. 湖南文理学院学报(自然科学版), 2015, 0(2): 14-18. DOI: 10.3969/j.issn.1672-6146.2015.02.006 |
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| 作者姓名： | 刘国永 李桂花 |
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| 作者单位： | 中北大学 数学系，山西 太原，030051 |
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| 摘 要： | 利用定义法给出SEIR模型的基本再生数,得到了各类平衡点存在的条件。利用Routh-Hurwitz判据证明了地方病平衡点*P是局部渐近稳定的;利用第二加性复合矩阵证明了地方病平衡点*P全局稳定性的充分条件。
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| 关 键 词： | 饱和发生率 治疗 基本再生数 稳定性 |
Analysis of an SEIR epidemic model with saturated rate and treatment |
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| Abstract: | The basic reproduction number of the model is given by using the definition, and the existing threshold conditions of all kinds of the equilibrium points are obtained. Locally asymptotic stability of the endemic equilibrium *P is proven by using the Routh-Hurwitz criterion, and the sufficient conditions of global asymptotic stability of the endemic equilibrium *P is also obtained by using the second additive compound matrix. |
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| Keywords: | saturated rate treatment basic reproduction number stability |
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