| 媒体报道下随机SIQS流行病模型的动态行为研究 |
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| 引用本文： | 胡晶晶,李彩凤,韦煜明,彭华勤.媒体报道下随机SIQS流行病模型的动态行为研究[J].上海师范大学学报(自然科学版),2019,48(2):129-140. |
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| 作者姓名： | 胡晶晶 李彩凤 韦煜明 彭华勤 |
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| 作者单位： | 广西师范大学 数学与统计学院, 广西 桂林 541004,河池学院 数学与统计学院, 广西 宜州 546300,广西师范大学 数学与统计学院, 广西 桂林 541004,广西师范大学 数学与统计学院, 广西 桂林 541004 |
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| 基金项目： | The National Natural Science Foundation of China (11771104);National Natural Science Foundation of Guangxi (2018GXNSFAA294084,2018GXNSFBA281140);Innovation Project of Guangxi Graduate Education (XYCSZ2019083,JGY2019030) |
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| 摘 要： | 研究了媒体报道干预策略下的随机SIQS流行病模型.构造合适的Lyapunov函数，使用Itô公式和马尔可夫半群理论，证明了基本再生数R0s可用于控制随机流行病模型的动态行为，即如果再生数R0s<1，并且在其他条件下，疾病将消亡；如果再生数R0s>1，并且在其他条件下，疾病是持久性的.结论表明：大的白噪声可以抑制疾病的爆发，这为制定有用的控制策略来调节疾病的动态行为提供有效帮助.最后通过数值模拟验证了这一结果.
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| 关 键 词： | 媒体报道 随机SIQS流行病模型 马尔可夫半群 基本再生数 |
| 收稿时间： | 2019/2/16 0:00:00 |
The dynamical behavior of a stochastic SIQS epidemic model under media coverage |
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| HU Jingjing,LI Caifeng,WEI Yuming and PENG Huaqin.The dynamical behavior of a stochastic SIQS epidemic model under media coverage[J].Journal of Shanghai Normal University(Natural Sciences),2019,48(2):129-140. |
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| Authors: | HU Jingjing LI Caifeng WEI Yuming and PENG Huaqin |
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| Institution: | College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, Guangxi, China,College of Mathematics and Statistics, Hechi University, Yizhou 546300, Guangxi, China,College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, Guangxi, China and College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, Guangxi, China |
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| Abstract: | In this paper,we are concerned with a stochastic SIQS epidemic disease model under media coverage intervention strategy.By constructing suitable Lyapunov function and using Itô formula and Markov semigroup theory,we show that the basic reproduction number R0s can be used to control the dynamics of the stochastic epidemic model.The conclusions are that if R0s<1 and under other conditions,the disease dies out;if R0s>1 and under other conditions,the disease is persistent.The results also show that large noise can suppress the disease outbreak,which provides us some useful control strategies to regulate the dynamical behavior of the disease.In the end,the theoretical results are illustrated by numerical simulations. |
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| Keywords: | media coverage stochastic SIQS epidemic model Markov semigroup basic reproduction number |
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