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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 3458965, 6 pages
Research Article

Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate

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

Received 23 October 2015; Accepted 5 January 2016

Academic Editor: Amit Chakraborty

Copyright © 2016 Maoxing Liu 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.


An epidemic model with media is proposed to describe the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that the media has its effect when the number of the infected exceeds a certain critical level. Furthermore, it is assumed that the impact of the media on the contact transmission is described by an exponential function. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity, a unique endemic equilibrium exists, which is also globally asymptotically stable. Our analysis implies that media coverage plays an important role in controlling the spread of the disease.