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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 2340549, 9 pages
https://doi.org/10.1155/2017/2340549
Research Article

Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate

Department of Mathematics and Physics, Bengbu University, Bengbu 233030, China

Correspondence should be addressed to Juan Liu

Received 16 February 2017; Accepted 28 March 2017; Published 9 May 2017

Academic Editor: Lu-Xing Yang

Copyright © 2017 Juan Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with a delayed SEIS (Susceptible-Exposed-Infectious-Susceptible) epidemic model with a changing delitescence and nonlinear incidence rate. First of all, local stability of the endemic equilibrium and the existence of a Hopf bifurcation are studied by choosing the time delay as the bifurcation parameter. Directly afterwards, properties of the Hopf bifurcation are determined based on the normal form theory and the center manifold theorem. At last, numerical simulations are carried out to illustrate the obtained theoretical results.