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