A note on the global properties of an age-structured viral dynamic model with multiple target cell populations
Some viruses can infect different classes of cells. The age of infection can affect the dynamics of infected cells and viral production. Here we develop a viral dynamic model with the age of infection and multiple target cell populations. Using the methods of semigroup and Lyapunov function, we stud...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017044 |
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| author | Shaoli Wang Jianhong Wu Libin Rong |
| author_facet | Shaoli Wang Jianhong Wu Libin Rong |
| author_sort | Shaoli Wang |
| collection | DOAJ |
| description | Some viruses can infect different classes of cells. The age of infection can affect the dynamics of infected cells and viral production. Here we develop a viral dynamic model with the age of infection and multiple target cell populations. Using the methods of semigroup and Lyapunov function, we study the global asymptotic property of the steady states of the model. The results show that when the basic reproductive number falls below 1, the infection is predicted to die out. When the basic reproductive number exceeds 1, there exists a unique infected steady state which is globally asymptotically stable. The model can be extended to study virus dynamics with multiple compartments or coinfection by multiple types of viruses. We also show that under some scenarios the age-structured model can be reduced to an ordinary differential equation system with or without time delays. |
| format | Article |
| id | doaj-art-c8a92f7bf49948008eb0d181b2af97a6 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c8a92f7bf49948008eb0d181b2af97a62025-01-24T02:39:48ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-05-0114380582010.3934/mbe.2017044A note on the global properties of an age-structured viral dynamic model with multiple target cell populationsShaoli Wang0Jianhong Wu1Libin Rong2School of Mathematics and Statistics, Henan University, Kaifeng 475001, Henan, ChinaCentre for Disease Modelling, York University, Toronto, Ontario, M3J 1P3, CanadaDepartment of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USASome viruses can infect different classes of cells. The age of infection can affect the dynamics of infected cells and viral production. Here we develop a viral dynamic model with the age of infection and multiple target cell populations. Using the methods of semigroup and Lyapunov function, we study the global asymptotic property of the steady states of the model. The results show that when the basic reproductive number falls below 1, the infection is predicted to die out. When the basic reproductive number exceeds 1, there exists a unique infected steady state which is globally asymptotically stable. The model can be extended to study virus dynamics with multiple compartments or coinfection by multiple types of viruses. We also show that under some scenarios the age-structured model can be reduced to an ordinary differential equation system with or without time delays.https://www.aimspress.com/article/doi/10.3934/mbe.2017044age structureglobal asymptotic propertylyapunov functionsemigroupmultiple compartments |
| spellingShingle | Shaoli Wang Jianhong Wu Libin Rong A note on the global properties of an age-structured viral dynamic model with multiple target cell populations Mathematical Biosciences and Engineering age structure global asymptotic property lyapunov function semigroup multiple compartments |
| title | A note on the global properties of an age-structured viral dynamic model with multiple target cell populations |
| title_full | A note on the global properties of an age-structured viral dynamic model with multiple target cell populations |
| title_fullStr | A note on the global properties of an age-structured viral dynamic model with multiple target cell populations |
| title_full_unstemmed | A note on the global properties of an age-structured viral dynamic model with multiple target cell populations |
| title_short | A note on the global properties of an age-structured viral dynamic model with multiple target cell populations |
| title_sort | note on the global properties of an age structured viral dynamic model with multiple target cell populations |
| topic | age structure global asymptotic property lyapunov function semigroup multiple compartments |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017044 |
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