Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 653937, 21 pages
Research Article

Complex Dynamics of Discrete SEIS Models with Simple Demography

1Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China
2Department of Mathematical Sciences, Montclair State University, Montclair, NJ 07043, USA

Received 29 May 2011; Revised 23 August 2011; Accepted 23 August 2011

Academic Editor: Elmetwally Elabbasy

Copyright © 2011 Hui Cao 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.


We investigate bifurcations and dynamical behaviors of discrete SEIS models with exogenous reinfections and a variety of treatment strategies. Bifurcations identified from the models include period doubling, backward, forward-backward, and multiple backward bifurcations. Multiple attractors, such as bistability and tristability, are observed. We also estimate the ultimate boundary of the infected regardless of initial status. Our rigorously mathematical analysis together with numerical simulations show that epidemiological factors alone can generate complex dynamics, though demographic factors only support simple equilibrium dynamics. Our model analysis supports and urges to treat a fixed percentage of exposed individuals.