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Liu, W.M., Hethcote, H.W. and Levin, S.A. (1987) Dynamical Behavior of Epidemiological Models with Nonlinear Incidence Rates. Mathematical Biosciences, 25, 359-380.

has been cited by the following article:

• 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.