Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate. (21st January 2016)

• Record Type: Journal Article
• Authors: Liu, Maoxing; Chang, Yuting; Zuo, Lixia
• Other Names: Chakraborty Amit Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2016(2016)
• Publication Date: 2016-01-21
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2016/3458965
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : 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.