Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/3458965 |
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| _version_ | 1849692428730105856 |
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| author | Maoxing Liu Yuting Chang Lixia Zuo |
| author_facet | Maoxing Liu Yuting Chang Lixia Zuo |
| author_sort | Maoxing Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-edb7873ca2db4959bbff2247173fe37a |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-edb7873ca2db4959bbff2247173fe37a2025-08-20T03:20:43ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/34589653458965Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission RateMaoxing Liu0Yuting Chang1Lixia Zuo2Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaAn 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.http://dx.doi.org/10.1155/2016/3458965 |
| spellingShingle | Maoxing Liu Yuting Chang Lixia Zuo Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate Discrete Dynamics in Nature and Society |
| title | Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate |
| title_full | Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate |
| title_fullStr | Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate |
| title_full_unstemmed | Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate |
| title_short | Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate |
| title_sort | modelling the impact of media in controlling the diseases with a piecewise transmission rate |
| url | http://dx.doi.org/10.1155/2016/3458965 |
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