Author(s)

Xiaomei Ren, Tiansi Zhang

College of Science, University of Shanghai for Science and Technology, Shanghai, China.

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.

SEIR Model, the Ratio-Dependent Transmission Rate, Basic Reproduction Number, Equilibrium, Global Stability

Ren, X. and Zhang, T. (2017) Global Analysis of an SEIR Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate. Journal of Applied Mathematics and Physics, 5, 2311-2319. doi: 10.4236/jamp.2017.512188.