TITLE:
Global Analysis of an SEIR Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate
AUTHORS:
Xiaomei Ren, Tiansi Zhang
KEYWORDS:
SEIR Model, the Ratio-Dependent Transmission Rate, Basic Reproduction Number, Equilibrium, Global Stability
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.12,
December
5,
2017
ABSTRACT: 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.