| 一类具有饱和发生率和心理作用的随机SIR传染病模型 |
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| 引用本文： | 赵彦军,李辉来,李文轩.一类具有饱和发生率和心理作用的随机SIR传染病模型[J].吉林大学学报(理学版),2021,59(1):20-26. |
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| 作者姓名： | 赵彦军 李辉来 李文轩 |
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| 作者单位： | 1. 东北师范大学人文学院 数学系, 长春 130117; 2. 吉林大学 数学学院, 长春 130012 |
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| 摘 要： | 考虑一类受环境噪声影响, 具有饱和发生率和心理作用的随机SIR传染病模型. 通过构造Lyapunov函数并利用Ito公式, 得到该模型正解的全局存在唯一性, 并证明： 当随机基本再生数R*≤1时, 无病平衡点是随机渐近稳定的, 此时疾病将灭绝； 当R*>1时, 疾病将随机持续下去. 数值模拟结果验证了理论结果的正确性.
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| 关 键 词： | 随机SIR传染病模型 饱和发生率 It公式 灭绝性 持久性 |
| 收稿时间： | 2020-06-29 |
A Class of Stochastic SIR Epidemic Model with Saturated Incidence and Psychological Effect |
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| ZHAO Yanjun,LI Huilai,LI Wenxuan.A Class of Stochastic SIR Epidemic Model with Saturated Incidence and Psychological Effect[J].Journal of Jilin University: Sci Ed,2021,59(1):20-26. |
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| Authors: | ZHAO Yanjun LI Huilai LI Wenxuan |
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| Institution: | 1. Department of Mathematics, College of Humanities and Sciences of Northeast Normal University, Changchun 130117, China;
2. College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | We considered a class of stochastic SIR epidemic model with saturated incidence and psychological effect by white noise in the environment. By constructing Lyapunov function and applying Ito formula, the global existence and uniqueness of the positive solution was obtained. We prove that when stochastic basic reproduction number R*≤1, the disease-free equilibrium is stochastically asymptotical stability, which means the disease will be extinction; if R*>1, the disease will be existence stochastically. The numerical simulation results verify the correctness of the theoretical results. |
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| Keywords: | stochastic SIR epidemic model saturated incidence Ito formula extinction persistence |
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