胡晶晶 李彩鳳 韋煜明 彭華勤

摘 要： 研究了媒體報道干預策略下的隨機SIQS流行病模型.構造合適的 Lyapunov 函數(shù)，使用It公式和馬爾可夫半群理論，證明了基本再生數(shù)Rs0可用于控制隨機流行病模型的動態(tài)行為，即如果再生數(shù)Rs0<1，并且在其他條件下，疾病將消亡;如果再生數(shù)Rs0>1，并且在其他條件下，疾病是持久性的.結論表明：大的白噪聲可以抑制疾病的爆發(fā)，這為制定有用的控制策略來調節(jié)疾病的動態(tài)行為提供有效幫助.最后通過數(shù)值模擬驗證了這一結果.

關鍵詞： 媒體報道; 隨機SIQS流行病模型; 馬爾可夫半群; 基本再生數(shù)

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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