Rich Dynamics of an Epidemic Model with Saturation Recovery
A SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/314958 |
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| _version_ | 1832564609671757824 |
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| author | Hui Wan Jing-an Cui |
| author_facet | Hui Wan Jing-an Cui |
| author_sort | Hui Wan |
| collection | DOAJ |
| description | A SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf bifurcation, are analyzed. Our results suggest that the model considering the impact of limited medical resource may exhibit vital dynamics, such as bistability and periodicity when the basic reproduction number ℝ0 is less than unity, which implies that the basic reproductive number itself is not enough to describe whether the disease will prevail or not and a subthreshold number is needed. It is also shown that a sufficient number of sickbeds and other medical resources are very important for disease control and eradication. Considering the costs, we provide a method to estimate a suitable treatment capacity for a disease in a region. |
| format | Article |
| id | doaj-art-5ffae8498b6347c3bc0d01e0668751bf |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5ffae8498b6347c3bc0d01e0668751bf2025-02-03T01:10:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/314958314958Rich Dynamics of an Epidemic Model with Saturation RecoveryHui Wan0Jing-an Cui1Jiangsu Key Laboratory for NSLSCS, School of Mathematics, Nanjing Normal University, Nanjing 210046, ChinaSchool of Sciences, Beijing University of Civil Engineering and Architecture, Beijing 100044, ChinaA SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf bifurcation, are analyzed. Our results suggest that the model considering the impact of limited medical resource may exhibit vital dynamics, such as bistability and periodicity when the basic reproduction number ℝ0 is less than unity, which implies that the basic reproductive number itself is not enough to describe whether the disease will prevail or not and a subthreshold number is needed. It is also shown that a sufficient number of sickbeds and other medical resources are very important for disease control and eradication. Considering the costs, we provide a method to estimate a suitable treatment capacity for a disease in a region.http://dx.doi.org/10.1155/2013/314958 |
| spellingShingle | Hui Wan Jing-an Cui Rich Dynamics of an Epidemic Model with Saturation Recovery Journal of Applied Mathematics |
| title | Rich Dynamics of an Epidemic Model with Saturation Recovery |
| title_full | Rich Dynamics of an Epidemic Model with Saturation Recovery |
| title_fullStr | Rich Dynamics of an Epidemic Model with Saturation Recovery |
| title_full_unstemmed | Rich Dynamics of an Epidemic Model with Saturation Recovery |
| title_short | Rich Dynamics of an Epidemic Model with Saturation Recovery |
| title_sort | rich dynamics of an epidemic model with saturation recovery |
| url | http://dx.doi.org/10.1155/2013/314958 |
| work_keys_str_mv | AT huiwan richdynamicsofanepidemicmodelwithsaturationrecovery AT jingancui richdynamicsofanepidemicmodelwithsaturationrecovery |