| 包含非线性发生率和预防接种的随机SIRS传染病模型 |
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| 引用本文： | 热木孜亚.热布哈提,夏米西努尔.阿布都热合曼.包含非线性发生率和预防接种的随机SIRS传染病模型[J].新疆大学学报(理工版),2014(1):57-63. |
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| 作者姓名： | 热木孜亚.热布哈提 夏米西努尔.阿布都热合曼 |
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| 作者单位： | 新疆大学数学与系统科学学院,新疆乌鲁木齐830046 |
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| 基金项目： | This work was suooorted by The National Natural Science Foundation of ER.China（11261056）. |
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| 摘 要： | 讨论了非持续免疫SIRS传染病模型的全局性。这里研究的SIRS包含了预防接种和非线性发生率及因病死忙率。由全局存在性和正解可以看出，以概率稳定性和全局随机渐进稳定性在强烈的白噪音扰动条件下成立。
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| 关 键 词： | 传染病模型 Lyapunov函数 伊藤公式 以概率全局稳定性 随机渐进稳定性 几乎指数稳定性 |
Stochastic SIRS Epidemic Model with Generalized Nonlinear Incidence and Vaccination |
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| Affiliation: | Ramziya Rifhat, Xamxinur Abdurahman (College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China) |
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| Abstract: | This paper deals with global dynamics of an SIRS epidemic model for infection with nonpermanent acquired immunity. The SIRS model studied here incorporates a preventive vaccination and generalized non-linear incidence rate as well as the disease-related death. The stochastic version, the global existence and positivity of the solution is showed, the global stability in probability and stochastically asymptotically stable in the large is proved under suitable condition on the intensity of the white noise perturbation. |
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| Keywords: | Epidemic model Lypunov function Ito’s formula Global stability in probability Stochastic asymptotic stability Almost sure exponential stability |
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