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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 940841, 8 pages
http://dx.doi.org/10.1155/2014/940841
Research Article

Effect of Awareness Programs on the Epidemic Outbreaks with Time Delay

Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China

Received 25 February 2014; Revised 12 June 2014; Accepted 13 June 2014; Published 13 July 2014

Academic Editor: Zhichun Yang

Copyright © 2014 Lixia Zuo and Maoxing Liu. 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.

Abstract

An epidemic model with time delay has been proposed and analyzed. In this model the effect of awareness programs driven by media on the prevalence of an infectious disease is studied. It is assumed that pathogens are transmitted via direct contact between the susceptible and the infective populations and further assumed that the growth rate of cumulative density of awareness programs increases at a rate proportional to the infective population. The model is analyzed by using stability theory of differential equations and numerical simulations. Both equilibria have been proved to be globally asymptotically stable. The results we obtained and numerical simulations suggest the increasing of the dissemination rate and implementation rate can reduce the proportion of the infective population.