| 具有变化潜伏期的水源性疾病模型稳定性分析 |
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| 引用本文： | 张海娥.具有变化潜伏期的水源性疾病模型稳定性分析[J].唐山学院学报,2013(6):10-12,60. |
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| 作者姓名： | 张海娥 |
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| 作者单位： | 唐山学院基础教学部,河北唐山063000 |
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| 基金项目： | 唐山市科技计划项目（12110233b）,河北省高校科技研究项目（Z2013016） |
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| 摘 要： | 建立了一类具有变化潜伏期的水源性疾病数学模型,得到了水源性疾病流行的阈值R0（基本再生数）.利用LaSalle不变集原理,通过构造新的Liapunov函数证明了平衡点的全局稳定性：当R0≤1时,系统的无病平衡点p0是全局渐近稳定的;当R0＞1时,系统的地方病平衡点p＊是全局渐近稳定的.最后利用数值模拟说明结论的正确性.
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| 关 键 词： | 水源性疾病 变化潜伏期 平衡点 全局渐近稳定 |
An Stability Analysis of the Models of Waterborne Diseases with Variable Latent Periods |
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| ZHANG Hai-e.An Stability Analysis of the Models of Waterborne Diseases with Variable Latent Periods[J].Journal of Tangshan College,2013(6):10-12,60. |
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| Authors: | ZHANG Hai-e |
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| Institution: | ZHANG Hai-e (Department of Basic Science,Tangshan College, Tangshan 063000, China) |
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| Abstract: | The mathematical model of waterborne diseases with variable latent periods should be established in order to find out the epidemic threshold of waterborne diseases R0 （basic reproduc-tive number）. By LaSalle Invariance Principle, the global stability of the equilibrium is proved by means of defining a new Liapunov function., when R0 ≤ 1, the disease-free equilibrium of the system P0 is globally asymptotically stable; when R0〉1, the endemic equilibrium of the system p ^＊ is globally asymptotically stable. Some numerical simulations are also carried out to prove the correctness of the conclusion. |
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| Keywords: | waterborne disease variable latent period equilibrium globally asymptotically stability |
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