$R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission
In this paper, we study an age-structured SIS epidemic model with periodicity and vertical transmission. We show that the spectral radius of the Fréchet derivative of a nonlinear integral operator plays the role of a threshold value for the global behavior of the model, that is, if the value is less...
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AIMS Press
2014-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.929 |
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| author | Toshikazu Kuniya Mimmo Iannelli |
| author_facet | Toshikazu Kuniya Mimmo Iannelli |
| author_sort | Toshikazu Kuniya |
| collection | DOAJ |
| description | In this paper, we study an age-structured SIS epidemic model with periodicity and vertical transmission. We show that the spectral radius of the Fréchet derivative of a nonlinear integral operator plays the role of a threshold value for the global behavior of the model, that is, if the value is less than unity, then the disease-free steady state of the model is globally asymptotically stable, while if the value is greater than unity, then the model has a unique globally asymptotically stable endemic (nontrivial) periodic solution. We also show that the value can coincide with the well-know epidemiological threshold value, the basic reproduction number $\mathcal{R}_0$. |
| format | Article |
| id | doaj-art-1b86feb638a44d9fbff08697d80748d6 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-1b86feb638a44d9fbff08697d80748d62025-01-24T02:28:18ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-02-0111492994510.3934/mbe.2014.11.929$R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmissionToshikazu Kuniya0Mimmo Iannelli1Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914Dipartimento di Mathematica, Università di Trento, 38050 Povo (Trento)In this paper, we study an age-structured SIS epidemic model with periodicity and vertical transmission. We show that the spectral radius of the Fréchet derivative of a nonlinear integral operator plays the role of a threshold value for the global behavior of the model, that is, if the value is less than unity, then the disease-free steady state of the model is globally asymptotically stable, while if the value is greater than unity, then the model has a unique globally asymptotically stable endemic (nontrivial) periodic solution. We also show that the value can coincide with the well-know epidemiological threshold value, the basic reproduction number $\mathcal{R}_0$.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.929periodicityage-structurevertical transmissionbasic reproduction number.sis epidemic model |
| spellingShingle | Toshikazu Kuniya Mimmo Iannelli $R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission Mathematical Biosciences and Engineering periodicity age-structure vertical transmission basic reproduction number. sis epidemic model |
| title | $R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission |
| title_full | $R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission |
| title_fullStr | $R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission |
| title_full_unstemmed | $R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission |
| title_short | $R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission |
| title_sort | r 0 and the global behavior of an age structured sis epidemic model with periodicity and vertical transmission |
| topic | periodicity age-structure vertical transmission basic reproduction number. sis epidemic model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.929 |
| work_keys_str_mv | AT toshikazukuniya r0andtheglobalbehaviorofanagestructuredsisepidemicmodelwithperiodicityandverticaltransmission AT mimmoiannelli r0andtheglobalbehaviorofanagestructuredsisepidemicmodelwithperiodicityandverticaltransmission |