| 具有随机扰动的SISV模型的解的渐近性态 |
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| 引用本文： | 李云飞,徐瑞,王海彬.具有随机扰动的SISV模型的解的渐近性态[J].军械工程学院学报,2012(5):74-78. |
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| 作者姓名： | 李云飞 徐瑞 王海彬 |
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| 作者单位： | 军械工程学院基础部,河北石家庄050003 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 研究一类具有两种随机扰动的SISV传染病模型．对于第一种随机SISV模型，证明对任给的非负初值，该随机模型一定存在唯一的全局正解，并讨论该随机模型的解围绕确定性模型的无病平衡点的渐近行为；对于第二种随机SISV模型，通过构造适当的Lyapunov泛函证明该随机模型的解是随机渐近稳定的．
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| 关 键 词： | 随机扰动 It6公式 随机Lyapunov泛函 |
Asymptotic Behavior of an SISV Model with Stochastic Perturbation |
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| LI Yun-fei,XU Rui,WANG Hai-bin.Asymptotic Behavior of an SISV Model with Stochastic Perturbation[J].Journal of Ordnance Engineering College,2012(5):74-78. |
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| Authors: | LI Yun-fei XU Rui WANG Hai-bin |
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| Institution: | (Department of Basic Courses, Ordnance Engineering College, Shijiazhuang 050003, China) |
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| Abstract: | In this paper, we present an SISV epidemic model with two kinds of stochastic perturbations. For the first model, we prove that it has a unique positive solution for any nonnegative initial value. Mainly,we discuss how the solution goes around the infection-free equilibrium of deterministic system under some conditions. For the second model, by constructing a suitable Lyapunov functional, we show that the solution of this stochastic model is stochastically asymptotically stable. |
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| Keywords: | stochastic perturbation Ito ＇ s formula stochastic Lyapunov functional |
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