Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 609306, 13 pages
doi:10.1155/2009/609306

Global dynamics of an epidemic model with a ratio-dependent nonlinear incidence rate

Abstract

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.