| 摘要: |
| 首先在双线性传染率βSI和不考虑种群之间迁移问题的SIS传染病模型的基础上，改进并增加种群迁移带来的影响条件，并建立一个更加符合实际意义的SIS传染病模型；在模型满足一定条件和符合实际意义下，平衡点存在的基础上，利用基本再生数R0和特征值理论分析得出，在R0≤1时无病平衡点局部渐近稳定的充分条件；进一步利用基本再生数R0和分块矩阵理论得出，当R0＞1时地方病平衡点局部渐近稳定的充分条件;模型的建立和研究进一步丰富了传染病模型。 |
| 关键词: SIS传染病模型 无病平衡点 地方病平衡点 基本再生数 |
| DOI： |
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| Local Stability Analysis on an SIS Epidemic Model in Patches Environment |
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YANG Wen chuan
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| Abstract: |
| On the basis of bilinear transmission rates βSI and SIS epidemic model in regardless of population dispersal, this paper designs a more practical SIS epidemic model by improving and adding influential condition caused by population dispersal. Meeting certain conditions with reality on the existence of equilibrium, by the basic productive number R0and eigenvalue theory this paper find that if R0＜1, the disease free equilibrium is local and asymptotically stable, while if R0＞1, the epidemic equilibrium is local and asymptotically stable. This model proposed enriches epidemic model types further. |
| Key words: SIS epidemic model disease free equilibrium epidemic equilibrium basic productive number |
