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Mathematical Problems in Engineering
Volume 2015, Article ID 235935, 10 pages
http://dx.doi.org/10.1155/2015/235935
Research Article

The Impact of Awareness Programs with Recruitment and Delay on the Spread of an Epidemic

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

Received 2 April 2014; Revised 18 July 2014; Accepted 1 August 2014

Academic Editor: Yuxin Zhao

Copyright © 2015 Lixia Zuo et al. 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

A compartment epidemic model with delay is given to discuss the impact of awareness programs on the spread and control of infectious diseases in a given region. It is assumed that there is a constant recruitment rate in the cumulative density of awareness programs, and further it is assumed that awareness programs can influence the susceptible to a limited extent. The system exhibits two equilibria: the disease-free equilibrium is stable if the basic reproduction number is less than unity for any delay and the unique endemic equilibrium exhibits Hopf-bifurcation under certain conditions. Numerical simulations prove the results of analysis and the significance of awareness programs in preventing and controlling the diseases, by investigating the relationship between the proportion of the infective and the dissemination rate and the implementation rate, respectively.