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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 314958, 9 pages
Research Article

Rich Dynamics of an Epidemic Model with Saturation Recovery

1Jiangsu Key Laboratory for NSLSCS, School of Mathematics, Nanjing Normal University, Nanjing 210046, China
2School of Sciences, Beijing University of Civil Engineering and Architecture, Beijing 100044, China

Received 18 January 2013; Accepted 26 March 2013

Academic Editor: Xinyu Song

Copyright © 2013 Hui Wan and Jing-an Cui. 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.


A SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf bifurcation, are analyzed. Our results suggest that the model considering the impact of limited medical resource may exhibit vital dynamics, such as bistability and periodicity when the basic reproduction number is less than unity, which implies that the basic reproductive number itself is not enough to describe whether the disease will prevail or not and a subthreshold number is needed. It is also shown that a sufficient number of sickbeds and other medical resources are very important for disease control and eradication. Considering the costs, we provide a method to estimate a suitable treatment capacity for a disease in a region.