人与人传染的有媒体影响因子的禽流感模型

摘要

建立人与人之间相互传染的有媒体影响因子的SI-SIR禽流感模型,并研究其动力学性态,得到判断疾病传播与否的阈值Ra和R0.利用Lyapunov函数、Dulac函数以及LaSalle不变原理等证明了当Ra＜1且R0＜1时,无病平衡点E0*是全局渐近稳定的;当Ra＜1且R0＞1时,边界平衡点E1*是全局渐近稳定的;当Ra＞1时,系统的正平衡点E2*是全局渐近稳定的.%The model of SI-SIR avian influenza with person-to-person transmission is established,the dynamic behavior of the model is studied,and two thresholds of determining the transmission are obtained.By using the Lyapunov function,Dulac function and LaSalle invariance principle,it shows that when Ra ＜1 and R0＜l,the disease free equilibrium is globally asymptotically stable;When R a ＜1 and R0 ＞ 1,the boundary equilibrium point El is globally asymptotically stable;When R a ＞1,the positive equilibrium point E;of the system is asymptotically stable.