Asymptotic Properties of a Hepatitis B Virus Infection Model with Time Delay
A hepatitis B virus infection model with time delay is discussed. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is studied. By using comparison arguments, it is proved that if the basic reproduction ratio is less than uni...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/182340 |
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| _version_ | 1832549517447135232 |
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| author | Xiaohong Tian Rui Xu |
| author_facet | Xiaohong Tian Rui Xu |
| author_sort | Xiaohong Tian |
| collection | DOAJ |
| description | A hepatitis B virus infection model with time delay is discussed. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is studied. By using comparison arguments, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproduction ratio is greater than unity, by means of an iteration technique, sufficient conditions are derived for the global asymptotic stability of the virus-infected equilibrium. Numerical simulations are carried out to illustrate the
theoretical results. |
| format | Article |
| id | doaj-art-66bcd1372cf34033833f9c5b3a5d1851 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-66bcd1372cf34033833f9c5b3a5d18512025-02-03T06:11:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/182340182340Asymptotic Properties of a Hepatitis B Virus Infection Model with Time DelayXiaohong Tian0Rui Xu1Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 Heping West Road, Shijiazhuang 050003, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 Heping West Road, Shijiazhuang 050003, ChinaA hepatitis B virus infection model with time delay is discussed. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is studied. By using comparison arguments, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproduction ratio is greater than unity, by means of an iteration technique, sufficient conditions are derived for the global asymptotic stability of the virus-infected equilibrium. Numerical simulations are carried out to illustrate the theoretical results.http://dx.doi.org/10.1155/2010/182340 |
| spellingShingle | Xiaohong Tian Rui Xu Asymptotic Properties of a Hepatitis B Virus Infection Model with Time Delay Discrete Dynamics in Nature and Society |
| title | Asymptotic Properties of a Hepatitis B Virus Infection Model with Time Delay |
| title_full | Asymptotic Properties of a Hepatitis B Virus Infection Model with Time Delay |
| title_fullStr | Asymptotic Properties of a Hepatitis B Virus Infection Model with Time Delay |
| title_full_unstemmed | Asymptotic Properties of a Hepatitis B Virus Infection Model with Time Delay |
| title_short | Asymptotic Properties of a Hepatitis B Virus Infection Model with Time Delay |
| title_sort | asymptotic properties of a hepatitis b virus infection model with time delay |
| url | http://dx.doi.org/10.1155/2010/182340 |
| work_keys_str_mv | AT xiaohongtian asymptoticpropertiesofahepatitisbvirusinfectionmodelwithtimedelay AT ruixu asymptoticpropertiesofahepatitisbvirusinfectionmodelwithtimedelay |