Table of Contents
ISRN Applied Mathematics
Volume 2013 (2013), Article ID 710643, 11 pages
http://dx.doi.org/10.1155/2013/710643
Research Article

Global Stability of an SEIS Epidemic Model with General Saturation Incidence

1Mathematics and OR Section, Xi’an Research Institute of High-Tech, Hongqing Town, Shaanxi, Xi’an 710025, China
2School of Mathematics and Statistics, Xi’an Jiaotong University, Shaanxi, Xi’an 710049, China

Received 18 February 2013; Accepted 11 March 2013

Academic Editors: J. R. Fernandez, C. Lu, E. Skubalska-Rafajlowicz, and F. Tadeo

Copyright © 2013 Hui Zhang et al. 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

We present an SEIS epidemic model with infective force in both latent period and infected period, which has different general saturation incidence rates. It is shown that the global dynamics are completely determined by the basic reproductive number . If , the disease-free equilibrium is globally asymptotically stable in by LaSalle’s Invariance Principle, and the disease dies out. Moreover, using the method of autonomous convergence theorem, we obtain that the unique epidemic equilibrium is globally asymptotically stable in , and the disease spreads to be endemic.