Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse
In this paper, an $SEIR$ epidemic model for an imperfect treatment disease with age-dependent latency and relapse is proposed. The model is well-suited to model tuberculosis. The basic reproduction number $R_{0}$ is calculated. We obtain the global behavior of the model in terms of $R_{0}$. If $R_{0...
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| Language: | English |
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017069 |
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| _version_ | 1832590056029683712 |
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| author | Shanjing Ren |
| author_facet | Shanjing Ren |
| author_sort | Shanjing Ren |
| collection | DOAJ |
| description | In this paper, an $SEIR$ epidemic model for an imperfect treatment disease with age-dependent latency and relapse is proposed. The model is well-suited to model tuberculosis. The basic reproduction number $R_{0}$ is calculated. We obtain the global behavior of the model in terms of $R_{0}$. If $R_{0} \lt 1$, the disease-free equilibrium is globally asymptotically stable, whereas if $R_{0} \gt 1$, a Lyapunov functional is used to show that the endemic equilibrium is globally stable amongst solutions for which the disease is present. |
| format | Article |
| id | doaj-art-726fff77b7984291acd577c7500b06df |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-726fff77b7984291acd577c7500b06df2025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61337136010.3934/mbe.2017069Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapseShanjing Ren0School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, ChinaIn this paper, an $SEIR$ epidemic model for an imperfect treatment disease with age-dependent latency and relapse is proposed. The model is well-suited to model tuberculosis. The basic reproduction number $R_{0}$ is calculated. We obtain the global behavior of the model in terms of $R_{0}$. If $R_{0} \lt 1$, the disease-free equilibrium is globally asymptotically stable, whereas if $R_{0} \gt 1$, a Lyapunov functional is used to show that the endemic equilibrium is globally stable amongst solutions for which the disease is present.https://www.aimspress.com/article/doi/10.3934/mbe.2017069age-structureliapunov functiontuberculosisinfection equilibriumglobal stability |
| spellingShingle | Shanjing Ren Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse Mathematical Biosciences and Engineering age-structure liapunov function tuberculosis infection equilibrium global stability |
| title | Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse |
| title_full | Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse |
| title_fullStr | Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse |
| title_full_unstemmed | Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse |
| title_short | Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse |
| title_sort | global stability in a tuberculosis model of imperfect treatment with age dependent latency and relapse |
| topic | age-structure liapunov function tuberculosis infection equilibrium global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017069 |
| work_keys_str_mv | AT shanjingren globalstabilityinatuberculosismodelofimperfecttreatmentwithagedependentlatencyandrelapse |