具有染病者输入的离散SIR传染病模型分析  

Analysis of a discrete-time SIR epidemic model with infected recruitment

作　　者：危敏剑[1,2] 董福安[1] 

机构地区：[1]空军工程大学理学院应用数学物理系 [2]94923部队

出　　处：《高校应用数学学报（A辑）》2011年第1期55-60,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11071256)

摘　　要：引入相应的概率建立了具有染病者输入的离散SIR传染病模型,确定了决定其动力学性态的阈值.在阈值之下模型仅存在无病平衡点,且无病平衡点是全局渐近稳定的;在阈值之上模型是一致持续的,有唯一的地方病平衡点存在,且地方病平衡点是局部渐近稳定的.The relevant probability is introduced to establish the discrete-time SIR epidemic model with infected recruiment and the threshold determining its dynamical behavior is found.For this model,below the threshold only the disease-free equilibrium exists which is globally asymptotically stable.Above the threshold the model is uniformly persistent and a unique endemic equilibrium exists which is locally asymptotically stable.

关 键 词：离散传染病模型 动力学性态 平衡点 稳定性 

分 类 号：O175.7[理学—数学]