Global stability of a multi-group model with vaccination age, distributed delay and random perturbation
A multi-group epidemic model withdistributed delay and vaccination age has been formulated and studied.Mathematical analysis shows that the global dynamics of the model is determinedby the basic reproduction number $\mathcal{R}_0$:the disease-free equilibrium is globally asymptotically stable if $...
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AIMS Press
2015-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1083 |
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| author | Jinhu Xu Yicang Zhou |
| author_facet | Jinhu Xu Yicang Zhou |
| author_sort | Jinhu Xu |
| collection | DOAJ |
| description | A multi-group epidemic model withdistributed delay and vaccination age has been formulated and studied.Mathematical analysis shows that the global dynamics of the model is determinedby the basic reproduction number $\mathcal{R}_0$:the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0\leq1$,and the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0>1$.Lyapunov functionals are constructed by the non-negative matrix theory and a novel grouping techniqueto establish the global stability.The stochastic perturbation of the model is studied and it is provedthat the endemic equilibrium of the stochastic model is stochastically asymptotically stablein the large under certain conditions. |
| format | Article |
| id | doaj-art-7d086b55dec241a387d1c4e910d88e2f |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7d086b55dec241a387d1c4e910d88e2f2025-01-24T02:33:19ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-05-011251083110610.3934/mbe.2015.12.1083Global stability of a multi-group model with vaccination age, distributed delay and random perturbationJinhu Xu0Yicang Zhou1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049A multi-group epidemic model withdistributed delay and vaccination age has been formulated and studied.Mathematical analysis shows that the global dynamics of the model is determinedby the basic reproduction number $\mathcal{R}_0$:the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0\leq1$,and the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0>1$.Lyapunov functionals are constructed by the non-negative matrix theory and a novel grouping techniqueto establish the global stability.The stochastic perturbation of the model is studied and it is provedthat the endemic equilibrium of the stochastic model is stochastically asymptotically stablein the large under certain conditions.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1083multi-groupdistributed delaystochastic perturbation.vaccination agelyapunov functional |
| spellingShingle | Jinhu Xu Yicang Zhou Global stability of a multi-group model with vaccination age, distributed delay and random perturbation Mathematical Biosciences and Engineering multi-group distributed delay stochastic perturbation. vaccination age lyapunov functional |
| title | Global stability of a multi-group model with vaccination age, distributed delay and random perturbation |
| title_full | Global stability of a multi-group model with vaccination age, distributed delay and random perturbation |
| title_fullStr | Global stability of a multi-group model with vaccination age, distributed delay and random perturbation |
| title_full_unstemmed | Global stability of a multi-group model with vaccination age, distributed delay and random perturbation |
| title_short | Global stability of a multi-group model with vaccination age, distributed delay and random perturbation |
| title_sort | global stability of a multi group model with vaccination age distributed delay and random perturbation |
| topic | multi-group distributed delay stochastic perturbation. vaccination age lyapunov functional |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1083 |
| work_keys_str_mv | AT jinhuxu globalstabilityofamultigroupmodelwithvaccinationagedistributeddelayandrandomperturbation AT yicangzhou globalstabilityofamultigroupmodelwithvaccinationagedistributeddelayandrandomperturbation |