媒体报道下随机SIQS流行病模型的动态行为研究

胡晶晶 李彩凤 韦煜明 彭华勤

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It公式和马尔可夫半群理论，证明了基本再生数Rs0可用于控制随机流行病模型的动态行为，即如果再生数Rs0<1，并且在其他条件下，疾病将消亡;如果再生数Rs0>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.

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

1 Introduction

The spread of diseases seriously hinders the development of society and economy[1].Hence，it′s necessary to control the spread of infectious diseases.HETHCOTE et al.[2] considers the following classic SIQS epidemic model：

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