| 一类具有饱和发生率和复发的随机SIRI模型的稳定性 |
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| 引用本文： | 穆宇光,徐,瑞.一类具有饱和发生率和复发的随机SIRI模型的稳定性[J].应用数学,2019,32(3):570-580. |
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| 作者姓名： | 穆宇光 徐 瑞 |
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| 作者单位： | 陆军工程大学石家庄校区军政基础系 |
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| 基金项目： | 国家自然科学基金(11871316,11371368) |
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| 摘 要： | 本文研究一类具有饱和发生率和复发的随机SIRI传染病模型.首先,我们证明随机系统存在唯一的全局正解.然后讨论无病平衡点的稳定性,并利用Lyapunov函数法证明流行病的灭绝.随后,我们得到疾病持久性的充分条件.最后,通过数值模拟说明结论的正确性.
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| 关 键 词： | 随机SIRI传染病模型 复发 饱和发生率 灭绝性 持久性 |
| 收稿时间： | 2018/7/26 0:00:00 |
Stability of a Stochastic SIRI Model with Saturated Incidence and Relapse |
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| MU Yuguang,XU Rui.Stability of a Stochastic SIRI Model with Saturated Incidence and Relapse[J].Mathematica Applicata,2019,32(3):570-580. |
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| Authors: | MU Yuguang XU Rui |
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| Institution: | (Military and Political Basic Department, Army Engineering University, Shijiazhuang050003, China) |
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| Abstract: | In this paper, a stochastic SIRI epidemiological model with saturation incidence and relapse is investigated. Firstly, we show that there exists a unique global positive solution of the stochastic system. Then we discuss the stability of the disease-free equilibrium state and show the extinction of epidemics by using Lyapunov functions. Subsequently, a sufficient condition for persistence has been established in the mean of the disease. Finally, some numerical simulations are carried out to confirm the analytical results. |
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| Keywords: | Stochastic SIRI epidemic model Relapse Saturation incidence Extinction Persistence in the mean |
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