Threshold dynamics of a periodic SIR model with delay in an infected compartment
Threshold dynamics of epidemic models in periodic environmentsattract more attention. But there are few papers which are concernedwith the case where the infected compartments satisfy a delaydifferential equation. For this reason, we investigate the dynamicalbehavior of a periodic SIR model with del...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.555 |
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| _version_ | 1832590136173395968 |
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| author | Zhenguo Bai |
| author_facet | Zhenguo Bai |
| author_sort | Zhenguo Bai |
| collection | DOAJ |
| description | Threshold dynamics of epidemic models in periodic environmentsattract more attention. But there are few papers which are concernedwith the case where the infected compartments satisfy a delaydifferential equation. For this reason, we investigate the dynamicalbehavior of a periodic SIR model with delay in an infectedcompartment. We first introduce the basic reproduction number$\mathcal {R}_0$ for the model, and then show that it can act as athreshold parameter that determines the uniform persistence orextinction of the disease. Numerical simulations are performed toconfirm the analytical results and illustrate the dependence of$\mathcal {R}_0$ on the seasonality and the latent period. |
| format | Article |
| id | doaj-art-a0e00aad2af5487891b0b1717d69e143 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a0e00aad2af5487891b0b1717d69e1432025-01-24T02:31:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-12-0112355556410.3934/mbe.2015.12.555Threshold dynamics of a periodic SIR model with delay in an infected compartmentZhenguo Bai0School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi 710071Threshold dynamics of epidemic models in periodic environmentsattract more attention. But there are few papers which are concernedwith the case where the infected compartments satisfy a delaydifferential equation. For this reason, we investigate the dynamicalbehavior of a periodic SIR model with delay in an infectedcompartment. We first introduce the basic reproduction number$\mathcal {R}_0$ for the model, and then show that it can act as athreshold parameter that determines the uniform persistence orextinction of the disease. Numerical simulations are performed toconfirm the analytical results and illustrate the dependence of$\mathcal {R}_0$ on the seasonality and the latent period.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.555periodicsolution.basic reproduction numberdelaythreshold dynamics |
| spellingShingle | Zhenguo Bai Threshold dynamics of a periodic SIR model with delay in an infected compartment Mathematical Biosciences and Engineering periodicsolution. basic reproduction number delay threshold dynamics |
| title | Threshold dynamics of a periodic SIR model with delay in an infected compartment |
| title_full | Threshold dynamics of a periodic SIR model with delay in an infected compartment |
| title_fullStr | Threshold dynamics of a periodic SIR model with delay in an infected compartment |
| title_full_unstemmed | Threshold dynamics of a periodic SIR model with delay in an infected compartment |
| title_short | Threshold dynamics of a periodic SIR model with delay in an infected compartment |
| title_sort | threshold dynamics of a periodic sir model with delay in an infected compartment |
| topic | periodicsolution. basic reproduction number delay threshold dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.555 |
| work_keys_str_mv | AT zhenguobai thresholddynamicsofaperiodicsirmodelwithdelayinaninfectedcompartment |