Open Access
2013 Rich Dynamics of an Epidemic Model with Saturation Recovery
Hui Wan, Jing-an Cui
J. Appl. Math. 2013: 1-9 (2013). DOI: 10.1155/2013/314958


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 0 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.


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Hui Wan. Jing-an Cui. "Rich Dynamics of an Epidemic Model with Saturation Recovery." J. Appl. Math. 2013 1 - 9, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.92057
MathSciNet: MR3049443
Digital Object Identifier: 10.1155/2013/314958

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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