An SEI infection model incorporating media impact
To study the impact of media coverage on spread and control of infectious diseases, we use a susceptible-exposed-infective (SEI) model, including individuals' behavior changes in their contacts due to the influences of media coverage, and fully investigate the model dynamics. We define the basi...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017068 |
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| author | Xuejuan Lu Shaokai Wang Shengqiang Liu Jia Li |
| author_facet | Xuejuan Lu Shaokai Wang Shengqiang Liu Jia Li |
| author_sort | Xuejuan Lu |
| collection | DOAJ |
| description | To study the impact of media coverage on spread and control of infectious diseases, we use a susceptible-exposed-infective (SEI) model, including individuals' behavior changes in their contacts due to the influences of media coverage, and fully investigate the model dynamics. We define the basic reproductive number $\Re_0$ for the model, and show that the modeled disease dies out regardless of initial infections when $\Re_0 \lt 1$, and becomes uniformly persistently endemic if $\Re_0 \gt 1$. When the disease is endemic and the influence of the media coverage is less than or equal to a critical number, there exists a unique endemic equilibrium which is asymptotical stable provided $\Re_0 $ is greater than and near one. However, if $\Re_0 $ is larger than a critical number, the model can undergo Hopf bifurcation such that multiple endemic equilibria are bifurcated from the unique endemic equilibrium as the influence of the media coverage is increased to a threshold value. Using numerical simulations we obtain results on the effects of media coverage on the endemic that the media coverage may decrease the peak value of the infectives or the average number of the infectives in different cases. We show, however, that given larger $\Re_0$, the influence of the media coverage may as well result in increasing the average number of the infectives, which brings challenges to the control and prevention of infectious diseases. |
| format | Article |
| id | doaj-art-dacb6294b5174595bd57f28c9722c8e0 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-dacb6294b5174595bd57f28c9722c8e02025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61317133510.3934/mbe.2017068An SEI infection model incorporating media impactXuejuan Lu0Shaokai Wang1Shengqiang Liu2Jia Li3Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaShenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USATo study the impact of media coverage on spread and control of infectious diseases, we use a susceptible-exposed-infective (SEI) model, including individuals' behavior changes in their contacts due to the influences of media coverage, and fully investigate the model dynamics. We define the basic reproductive number $\Re_0$ for the model, and show that the modeled disease dies out regardless of initial infections when $\Re_0 \lt 1$, and becomes uniformly persistently endemic if $\Re_0 \gt 1$. When the disease is endemic and the influence of the media coverage is less than or equal to a critical number, there exists a unique endemic equilibrium which is asymptotical stable provided $\Re_0 $ is greater than and near one. However, if $\Re_0 $ is larger than a critical number, the model can undergo Hopf bifurcation such that multiple endemic equilibria are bifurcated from the unique endemic equilibrium as the influence of the media coverage is increased to a threshold value. Using numerical simulations we obtain results on the effects of media coverage on the endemic that the media coverage may decrease the peak value of the infectives or the average number of the infectives in different cases. We show, however, that given larger $\Re_0$, the influence of the media coverage may as well result in increasing the average number of the infectives, which brings challenges to the control and prevention of infectious diseases.https://www.aimspress.com/article/doi/10.3934/mbe.2017068media impacthopf bifurcationstabilityinfectious disease |
| spellingShingle | Xuejuan Lu Shaokai Wang Shengqiang Liu Jia Li An SEI infection model incorporating media impact Mathematical Biosciences and Engineering media impact hopf bifurcation stability infectious disease |
| title | An SEI infection model incorporating media impact |
| title_full | An SEI infection model incorporating media impact |
| title_fullStr | An SEI infection model incorporating media impact |
| title_full_unstemmed | An SEI infection model incorporating media impact |
| title_short | An SEI infection model incorporating media impact |
| title_sort | sei infection model incorporating media impact |
| topic | media impact hopf bifurcation stability infectious disease |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017068 |
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