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

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DOI: 10.4236/jamp.2017.512188    395 Downloads   678 Views

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.

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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.

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