A note on dynamics of an age-of-infection cholera model
A recent paper [F. Brauer, Z. Shuai and P. van den Driessche, Dynamics of an age-of-infection cholera model, Math. Biosci. Eng., 10, 2013, 1335--1349.] presented a model for the dynamics of cholera transmission. The model is incorporated with both the infection age of infectious individuals and biol...
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AIMS Press
2015-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.227 |
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| author | Jinliang Wang Ran Zhang Toshikazu Kuniya |
| author_facet | Jinliang Wang Ran Zhang Toshikazu Kuniya |
| author_sort | Jinliang Wang |
| collection | DOAJ |
| description | A recent paper [F. Brauer, Z. Shuai and P. van den Driessche, Dynamics of an age-of-infection cholera model, Math. Biosci. Eng., 10, 2013, 1335--1349.] presented a model for the dynamics of cholera transmission. The model is incorporated with both the infection age of infectious individuals and biological age of pathogen in the environment. The basic reproduction number is proved to be a sharp threshold determining whether or not cholera dies out. The global stability for disease-free equilibrium and endemic equilibrium is proved by constructing suitable Lyapunov functionals. However, for the proof of the global stability of endemic equilibrium, we have to show first the relative compactness of the orbit generated by model in order to make use of the invariance principle. Furthermore, uniform persistence of system must be shown since the Lyapunov functional is possible to be infinite if$i(a, t)/i^* (a) =0$ on some age interval.In this note, we give a supplement to above paper with necessary mathematical arguments. |
| format | Article |
| id | doaj-art-d20337de1a9b4e938e840f89c8c5a33a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d20337de1a9b4e938e840f89c8c5a33a2025-01-24T02:34:06ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-09-0113122724710.3934/mbe.2016.13.227A note on dynamics of an age-of-infection cholera modelJinliang Wang0Ran Zhang1Toshikazu Kuniya2School of Mathematical Science, Heilongjiang University, Harbin 150080School of Mathematical Science, Heilongjiang University, Harbin 150080Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501A recent paper [F. Brauer, Z. Shuai and P. van den Driessche, Dynamics of an age-of-infection cholera model, Math. Biosci. Eng., 10, 2013, 1335--1349.] presented a model for the dynamics of cholera transmission. The model is incorporated with both the infection age of infectious individuals and biological age of pathogen in the environment. The basic reproduction number is proved to be a sharp threshold determining whether or not cholera dies out. The global stability for disease-free equilibrium and endemic equilibrium is proved by constructing suitable Lyapunov functionals. However, for the proof of the global stability of endemic equilibrium, we have to show first the relative compactness of the orbit generated by model in order to make use of the invariance principle. Furthermore, uniform persistence of system must be shown since the Lyapunov functional is possible to be infinite if$i(a, t)/i^* (a) =0$ on some age interval.In this note, we give a supplement to above paper with necessary mathematical arguments.https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.227global stabilitycholera modellyapunov functionaluniform persistence.age-of-infection |
| spellingShingle | Jinliang Wang Ran Zhang Toshikazu Kuniya A note on dynamics of an age-of-infection cholera model Mathematical Biosciences and Engineering global stability cholera model lyapunov functional uniform persistence. age-of-infection |
| title | A note on dynamics of an age-of-infection cholera model |
| title_full | A note on dynamics of an age-of-infection cholera model |
| title_fullStr | A note on dynamics of an age-of-infection cholera model |
| title_full_unstemmed | A note on dynamics of an age-of-infection cholera model |
| title_short | A note on dynamics of an age-of-infection cholera model |
| title_sort | note on dynamics of an age of infection cholera model |
| topic | global stability cholera model lyapunov functional uniform persistence. age-of-infection |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.227 |
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