Dynamics of an SIR Epidemic Model with Information Variable and Limited Medical Resources Revisited
The stability of the SIR epidemic model with information variable and limited medical resources was studied. When the basic reproduction ratio ℛ0<1, there exists the disease-free equilibrium and when the basic reproduction ratio ℛ0>1, we obtain the sufficient conditions of the existence of the...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/861710 |
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| _version_ | 1832567675240316928 |
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| author | Caijuan Yan Jianwen Jia Zhen Jin |
| author_facet | Caijuan Yan Jianwen Jia Zhen Jin |
| author_sort | Caijuan Yan |
| collection | DOAJ |
| description | The stability of the SIR epidemic model with
information variable and limited medical resources was studied. When the basic reproduction ratio ℛ0<1, there exists the disease-free equilibrium and when the basic reproduction ratio ℛ0>1, we obtain the sufficient conditions of the existence of the endemic equilibrium. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. A numerical analysis is given to show the effectiveness of the main results. |
| format | Article |
| id | doaj-art-abe540db677b4e399d77cf098216fc82 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-abe540db677b4e399d77cf098216fc822025-02-03T01:00:50ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/861710861710Dynamics of an SIR Epidemic Model with Information Variable and Limited Medical Resources RevisitedCaijuan Yan0Jianwen Jia1Zhen Jin2School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen 041004, ChinaSchool of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen 041004, ChinaDepartment of Mathematics, North University of China, Shanxi, Taiyuan 030051, ChinaThe stability of the SIR epidemic model with information variable and limited medical resources was studied. When the basic reproduction ratio ℛ0<1, there exists the disease-free equilibrium and when the basic reproduction ratio ℛ0>1, we obtain the sufficient conditions of the existence of the endemic equilibrium. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. A numerical analysis is given to show the effectiveness of the main results.http://dx.doi.org/10.1155/2014/861710 |
| spellingShingle | Caijuan Yan Jianwen Jia Zhen Jin Dynamics of an SIR Epidemic Model with Information Variable and Limited Medical Resources Revisited Discrete Dynamics in Nature and Society |
| title | Dynamics of an SIR Epidemic Model with Information Variable and Limited Medical Resources Revisited |
| title_full | Dynamics of an SIR Epidemic Model with Information Variable and Limited Medical Resources Revisited |
| title_fullStr | Dynamics of an SIR Epidemic Model with Information Variable and Limited Medical Resources Revisited |
| title_full_unstemmed | Dynamics of an SIR Epidemic Model with Information Variable and Limited Medical Resources Revisited |
| title_short | Dynamics of an SIR Epidemic Model with Information Variable and Limited Medical Resources Revisited |
| title_sort | dynamics of an sir epidemic model with information variable and limited medical resources revisited |
| url | http://dx.doi.org/10.1155/2014/861710 |
| work_keys_str_mv | AT caijuanyan dynamicsofansirepidemicmodelwithinformationvariableandlimitedmedicalresourcesrevisited AT jianwenjia dynamicsofansirepidemicmodelwithinformationvariableandlimitedmedicalresourcesrevisited AT zhenjin dynamicsofansirepidemicmodelwithinformationvariableandlimitedmedicalresourcesrevisited |