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一类具有非线性发生率的SI传染病模型的定性分析 被引量：1

Qualitative Analysis of an SI Epidemic Model with Nonlinear Incidence Rate
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摘要 研究一类具有非线性发生率的SI传染病模型.应用微分方程定性理论,给出了该系统极限环的存在性、唯一性以及无病平衡点和地方病平衡点的全局渐近稳定性的充分条件. An SI epidemic model with nonlinear incidence rate is investigated. By using the qualitative theory of ordinary differential equations, sufficient conditions are obtained for the existence and uniqueness of limit cycles and the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium to the proposed model.
作者 杜艳可 徐瑞 段立江
机构地区 军械工程学院基础部
出处 《大学数学》 2011年第5期71-75,共5页 College Mathematics
基金 军械工程学院科研基金资助(YJJXM0609 JCB0803)
关键词 传染病模型 平衡点 极限环 全局稳定性 epidemic model equilibrium limit cycle global stability
分类号 O175.13 [理学—基础数学]
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参考文献7

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  • 2Hyman J M, Li J. An intuitive formulation for the reproductive number for the spread of diseases in heterogeneous populations [J].Math. Biosci. , 2000, 167(1): 65-86.
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二级参考文献10

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  • 2Hyman J M, Li J. An intuitive formulation for the reproductive number for the spread of diseases in heterogeneous populations [J]. Math Biosci, 2000 , 167(1): 65-86.
  • 3Ma Z, Liu J P, Li J. Stability analysis for differential infectivity epidemic models [J]. Nonlinear Analysis:Real World Applications, 2003 , 4(5): 841-856.
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  • 9陈军杰,张南松.具有常恢复率的艾滋病梯度传染模型[J].应用数学学报,2002,25(3):538-546. 被引量：13
  • 10San-ling,Zhi-enMa,ZhenJin.Persistence and Periodic Solution on a Nonautonomous SIS Model with Delays[J].Acta Mathematicae Applicatae Sinica,2003,19(1):167-176. 被引量：5

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大学数学
2011年 第5期

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