Global Analysis of an SEIR Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate  

作　　者：Xiaomei Ren Tiansi Zhang 

机构地区：[1]College of Science, University of Shanghai for Science and Technology, Shanghai, China

出　　处：《Journal of Applied Mathematics and Physics》2017年第12期2311-2319,共9页应用数学与应用物理（英文）

摘　　要：In this paper, a SEIR model with ratio-dependent transmission rate in the form ?is studied and the basic reproduction number which determines the disease’s extinction or continued existence is obtained. By constructing the proper Lyapunov function, we prove that if R0 ≤ 1, the disease-free equilibrium point of the model is globally asymptotically stable and the disease always dies out;if R0 > 1, the endemic equilibrium point is globally asymptotically stable and the disease persists.In this paper, a SEIR model with ratio-dependent transmission rate in the form ?is studied and the basic reproduction number which determines the disease’s extinction or continued existence is obtained. By constructing the proper Lyapunov function, we prove that if R0 ≤ 1, the disease-free equilibrium point of the model is globally asymptotically stable and the disease always dies out;if R0 > 1, the endemic equilibrium point is globally asymptotically stable and the disease persists.

关 键 词：SEIR Model the RATIO-DEPENDENT TRANSMISSION RATE Basic REPRODUCTION NUMBER EQUILIBRIUM Global Stability 

分 类 号：O1[理学—数学]