| 具有隔离接种且传染率为非线性的传染病模型的稳定性 |
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| 引用本文： | 殷蓉蓉,胡志兴.具有隔离接种且传染率为非线性的传染病模型的稳定性[J].北京轻工业学院学报,2009(3):74-77. |
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| 作者姓名： | 殷蓉蓉 胡志兴 |
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| 作者单位： | 北京科技大学应用科学学院,北京100083 |
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| 基金项目： | 国家自然科学基金资助项目（10671011）. |
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| 摘 要： | 研究一类具有预防接种、隔离且传染率依赖于易感人口的SIQRS传染病模型，给出确定疾病消亡和持续生存的基本再生数σ．在一定条件下证明无病平衡点的全局稳定性，得到唯一地方病平衡点的存在性和局部渐近稳定条件．
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| 关 键 词： | 数学模型 传染病 基本再生数 平衡点 稳定性 |
STABILITY OF AN EPIDEMIC MODEL FOR NONLINEAR INFECTIOUS RATE WITH VACCINATION AND QUARANTINE |
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| YIN Rong-rong,HU Zhi-xing.STABILITY OF AN EPIDEMIC MODEL FOR NONLINEAR INFECTIOUS RATE WITH VACCINATION AND QUARANTINE[J].Journal of Beijing Institute of Light Industry,2009(3):74-77. |
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| Authors: | YIN Rong-rong HU Zhi-xing |
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| Affiliation: | ( School of Applied Science, University of Science and Technology Beijing, Beijing 10083, China ) |
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| Abstract: | An epidemic SIQRS model with vaccination, quarantine and nonlinear infectious rate is analyzed in this paper. Derived is a threshold σ which determines the existence of the infectious disease. In some conditions, we demonstrate that the disease free equilibrium is globally stable. The existence of a unique endemic equilibrium and the condition of local asymptotic stability are obtained. |
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| Keywords: | mathematical model infectious disease basic reproductive number equilibrium stability |
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