Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates
We investigate a class of multigroup epidemic models with general exposed distribution and nonlinear incidence rates. For a simpler case that assumes an identical natural death rate for all groups, and with a gamma distribution for exposed distribution is considered. Some sufficient conditions are o...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/354287 |
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| _version_ | 1832552500361691136 |
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| author | Ling Zhang Jingmei Pang Jinliang Wang |
| author_facet | Ling Zhang Jingmei Pang Jinliang Wang |
| author_sort | Ling Zhang |
| collection | DOAJ |
| description | We investigate a class of multigroup epidemic models with general exposed distribution and nonlinear incidence rates. For a simpler case that assumes an identical natural death rate for all groups, and with a gamma distribution for exposed distribution is considered. Some sufficient conditions are obtained to ensure that the global dynamics are completely determined by the basic production number R0. The proofs of the main results exploit the method of constructing Lyapunov functionals and a graph-theoretical technique in estimating the derivatives of Lyapunov functionals. |
| format | Article |
| id | doaj-art-5669e14476604eb187fbd32804b55c29 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5669e14476604eb187fbd32804b55c292025-02-03T05:58:35ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/354287354287Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence RatesLing Zhang0Jingmei Pang1Jinliang Wang2School of Science, Department of Fundamental Mathematics, Jiamusi University, Jiamusi 154007, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaWe investigate a class of multigroup epidemic models with general exposed distribution and nonlinear incidence rates. For a simpler case that assumes an identical natural death rate for all groups, and with a gamma distribution for exposed distribution is considered. Some sufficient conditions are obtained to ensure that the global dynamics are completely determined by the basic production number R0. The proofs of the main results exploit the method of constructing Lyapunov functionals and a graph-theoretical technique in estimating the derivatives of Lyapunov functionals.http://dx.doi.org/10.1155/2013/354287 |
| spellingShingle | Ling Zhang Jingmei Pang Jinliang Wang Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates Abstract and Applied Analysis |
| title | Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates |
| title_full | Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates |
| title_fullStr | Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates |
| title_full_unstemmed | Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates |
| title_short | Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates |
| title_sort | stability analysis of a multigroup epidemic model with general exposed distribution and nonlinear incidence rates |
| url | http://dx.doi.org/10.1155/2013/354287 |
| work_keys_str_mv | AT lingzhang stabilityanalysisofamultigroupepidemicmodelwithgeneralexposeddistributionandnonlinearincidencerates AT jingmeipang stabilityanalysisofamultigroupepidemicmodelwithgeneralexposeddistributionandnonlinearincidencerates AT jinliangwang stabilityanalysisofamultigroupepidemicmodelwithgeneralexposeddistributionandnonlinearincidencerates |