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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 609306, 13 pages
Research Article

Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate

College of Science, Shanghai University for Science and Technology, Shanghai 200093, China

Received 14 May 2009; Accepted 21 August 2009

Academic Editor: Antonia Vecchio

Copyright © 2009 Sanling Yuan and Bo Li. 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 study an epidemic model with a nonlinear incidence rate which describes the psychological effect of certain serious diseases on the community when the ratio of the number of infectives to that of the susceptibles is getting larger. The model has set up a challenging issue regarding its dynamics near the origin since it is not well defined there. By carrying out a global analysis of the model and studying the stabilities of the disease-free equilibrium and the endemic equilibrium, it is shown that either the number of infective individuals tends to zero as time evolves or the disease persists. Computer simulations are presented to illustrate the results.