Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay
The paper investigated an avian influenza virus propagation model with nonlinear incidence rate and delay based on SIR epidemic model. We regard delay as bifurcating parameter to study the dynamical behaviors. At first, local asymptotical stability and existence of Hopf bifurcation are studied; Hopf...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/242410 |
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| _version_ | 1832552011616223232 |
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| author | Yanhui Zhai Ying Xiong Xiaona Ma Haiyun Bai |
| author_facet | Yanhui Zhai Ying Xiong Xiaona Ma Haiyun Bai |
| author_sort | Yanhui Zhai |
| collection | DOAJ |
| description | The paper investigated an avian influenza virus propagation model with nonlinear incidence rate and delay based on SIR epidemic model. We regard delay as bifurcating parameter to study the dynamical behaviors. At first, local asymptotical stability and existence of Hopf bifurcation are studied; Hopf bifurcation occurs when time delay passes through a sequence of critical values. An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more, the global existence of periodic solutions is established by using a global Hopf bifurcation result. |
| format | Article |
| id | doaj-art-58c9d8a2c88b4ecabd76dc10522dc33f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-58c9d8a2c88b4ecabd76dc10522dc33f2025-02-03T05:59:50ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/242410242410Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and DelayYanhui Zhai0Ying Xiong1Xiaona Ma2Haiyun Bai3School of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaSchool of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaSchool of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaSchool of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaThe paper investigated an avian influenza virus propagation model with nonlinear incidence rate and delay based on SIR epidemic model. We regard delay as bifurcating parameter to study the dynamical behaviors. At first, local asymptotical stability and existence of Hopf bifurcation are studied; Hopf bifurcation occurs when time delay passes through a sequence of critical values. An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more, the global existence of periodic solutions is established by using a global Hopf bifurcation result.http://dx.doi.org/10.1155/2014/242410 |
| spellingShingle | Yanhui Zhai Ying Xiong Xiaona Ma Haiyun Bai Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay Abstract and Applied Analysis |
| title | Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay |
| title_full | Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay |
| title_fullStr | Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay |
| title_full_unstemmed | Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay |
| title_short | Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay |
| title_sort | global hopf bifurcation analysis for an avian influenza virus propagation model with nonlinear incidence rate and delay |
| url | http://dx.doi.org/10.1155/2014/242410 |
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