Dynamics of an infectious diseases with media/psychology induced non-smooth incidence
This paper proposes and analyzes a mathematical model on aninfectious disease system with a piecewise smooth incidence rateconcerning media/psychological effect. The proposed models extendthe classic models with media coverage by including a piecewisesmooth incidence rate to represent that the red...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.445 |
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| _version_ | 1832590159281913856 |
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| author | Yanni Xiao Tingting Zhao Sanyi Tang |
| author_facet | Yanni Xiao Tingting Zhao Sanyi Tang |
| author_sort | Yanni Xiao |
| collection | DOAJ |
| description | This paper proposes and analyzes a mathematical model on aninfectious disease system with a piecewise smooth incidence rateconcerning media/psychological effect. The proposed models extendthe classic models with media coverage by including a piecewisesmooth incidence rate to represent that the reduction factor becauseof media coverage depends on both the number of cases and the rateof changes in case number. On the basis of properties of Lambert Wfunction the implicitly defined model has been converted into apiecewise smooth system with explicit definition, and the globaldynamic behavior is theoretically examined. The disease-free isglobally asymptotically stable when a certain threshold is less thanunity, while the endemic equilibrium is globally asymptoticallystable for otherwise. The media/psychological impact although doesnot affect the epidemic threshold, delays the epidemic peak andresults in a lower size of outbreak (or equilibrium level ofinfected individuals). |
| format | Article |
| id | doaj-art-f12dc5d25194451e80486b34481b6c6f |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f12dc5d25194451e80486b34481b6c6f2025-01-24T02:25:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-12-0110244546110.3934/mbe.2013.10.445Dynamics of an infectious diseases with media/psychology induced non-smooth incidenceYanni Xiao0Tingting Zhao1Sanyi Tang2Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049This paper proposes and analyzes a mathematical model on aninfectious disease system with a piecewise smooth incidence rateconcerning media/psychological effect. The proposed models extendthe classic models with media coverage by including a piecewisesmooth incidence rate to represent that the reduction factor becauseof media coverage depends on both the number of cases and the rateof changes in case number. On the basis of properties of Lambert Wfunction the implicitly defined model has been converted into apiecewise smooth system with explicit definition, and the globaldynamic behavior is theoretically examined. The disease-free isglobally asymptotically stable when a certain threshold is less thanunity, while the endemic equilibrium is globally asymptoticallystable for otherwise. The media/psychological impact although doesnot affect the epidemic threshold, delays the epidemic peak andresults in a lower size of outbreak (or equilibrium level ofinfected individuals).https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.445outbreakepidemic threshold.media coveragesir epidemic model |
| spellingShingle | Yanni Xiao Tingting Zhao Sanyi Tang Dynamics of an infectious diseases with media/psychology induced non-smooth incidence Mathematical Biosciences and Engineering outbreak epidemic threshold. media coverage sir epidemic model |
| title | Dynamics of an infectious diseases with media/psychology induced non-smooth incidence |
| title_full | Dynamics of an infectious diseases with media/psychology induced non-smooth incidence |
| title_fullStr | Dynamics of an infectious diseases with media/psychology induced non-smooth incidence |
| title_full_unstemmed | Dynamics of an infectious diseases with media/psychology induced non-smooth incidence |
| title_short | Dynamics of an infectious diseases with media/psychology induced non-smooth incidence |
| title_sort | dynamics of an infectious diseases with media psychology induced non smooth incidence |
| topic | outbreak epidemic threshold. media coverage sir epidemic model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.445 |
| work_keys_str_mv | AT yannixiao dynamicsofaninfectiousdiseaseswithmediapsychologyinducednonsmoothincidence AT tingtingzhao dynamicsofaninfectiousdiseaseswithmediapsychologyinducednonsmoothincidence AT sanyitang dynamicsofaninfectiousdiseaseswithmediapsychologyinducednonsmoothincidence |