Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures
In this paper, we formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model with perturbation. We show that if a threshold value, which corresponds to the well-known basic...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2014-08-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1375 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590160186834944 |
|---|---|
| author | Toshikazu Kuniya Yoshiaki Muroya Yoichi Enatsu |
| author_facet | Toshikazu Kuniya Yoshiaki Muroya Yoichi Enatsu |
| author_sort | Toshikazu Kuniya |
| collection | DOAJ |
| description | In this paper, we formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model with perturbation. We show that if a threshold value, which corresponds to the well-known basic reproduction number $R_0$, is less than or equal to unity, then the disease-free equilibrium of the model is globally asymptotically stable. We also show that if the threshold value is greater than unity, then the model is uniformly persistent and has an endemic equilibrium. Moreover, using a Lyapunov functional technique, we obtain a sufficient condition under which the endemic equilibrium is globally asymptotically stable. The sufficient condition is satisfied if the transmission coefficients in the same groups are large or the per capita recovery rates are small. |
| format | Article |
| id | doaj-art-f64f42897a894fb5974fe329e50e732e |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f64f42897a894fb5974fe329e50e732e2025-01-24T02:29:00ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-08-011161375139310.3934/mbe.2014.11.1375Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structuresToshikazu Kuniya0Yoshiaki Muroya1Yoichi Enatsu2Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914In this paper, we formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model with perturbation. We show that if a threshold value, which corresponds to the well-known basic reproduction number $R_0$, is less than or equal to unity, then the disease-free equilibrium of the model is globally asymptotically stable. We also show that if the threshold value is greater than unity, then the model is uniformly persistent and has an endemic equilibrium. Moreover, using a Lyapunov functional technique, we obtain a sufficient condition under which the endemic equilibrium is globally asymptotically stable. The sufficient condition is satisfied if the transmission coefficients in the same groups are large or the per capita recovery rates are small.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1375multigroupsir epidemic modelpatchglobal asymptotic stabilitylyapunov functional. |
| spellingShingle | Toshikazu Kuniya Yoshiaki Muroya Yoichi Enatsu Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures Mathematical Biosciences and Engineering multigroup sir epidemic model patch global asymptotic stability lyapunov functional. |
| title | Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures |
| title_full | Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures |
| title_fullStr | Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures |
| title_full_unstemmed | Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures |
| title_short | Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures |
| title_sort | threshold dynamics of an sir epidemic model with hybrid of multigroup and patch structures |
| topic | multigroup sir epidemic model patch global asymptotic stability lyapunov functional. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1375 |
| work_keys_str_mv | AT toshikazukuniya thresholddynamicsofansirepidemicmodelwithhybridofmultigroupandpatchstructures AT yoshiakimuroya thresholddynamicsofansirepidemicmodelwithhybridofmultigroupandpatchstructures AT yoichienatsu thresholddynamicsofansirepidemicmodelwithhybridofmultigroupandpatchstructures |