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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 854528, 9 pages
http://dx.doi.org/10.1155/2014/854528
Research Article

Dynamical Behavior of a New Epidemiological Model

1School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
2Key Laboratory of Mathematics and Interdisciplinary Science of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou 510006, China

Received 29 October 2013; Revised 27 December 2013; Accepted 15 January 2014; Published 2 March 2014

Academic Editor: P. G. L. Leach

Copyright © 2014 Zizi Wang and Zhiming Guo. 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

A new epidemiological model is introduced with nonlinear incidence, in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain time . The existence, uniqueness, and stability of the disease-free equilibrium and endemic equilibrium are discussed. The basic reproductive number is given. The model is studied in two cases: with and without time delay. For the model without time delay, the disease-free equilibrium is globally asymptotically stable provided that ; if , then there exists a unique endemic equilibrium, and it is globally asymptotically stable. For the model with time delay, a sufficient condition is given to ensure that the disease-free equilibrium is locally asymptotically stable. Hopf bifurcation in endemic equilibrium with respect to the time is also addressed.