Global stability for a class of discrete SIR epidemic models
In this paper, we propose a class of discrete SIR epidemic models which are derived from SIR epidemic models with distributed delays by using a variation of the backward Euler method.Applying a Lyapunov functional technique, it is shown that the global dynamics of each discrete SIR epidemic model ar...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2010-03-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.347 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590184010481664 |
|---|---|
| author | Yoichi Enatsu Yukihiko Nakata Yoshiaki Muroya |
| author_facet | Yoichi Enatsu Yukihiko Nakata Yoshiaki Muroya |
| author_sort | Yoichi Enatsu |
| collection | DOAJ |
| description | In this paper, we propose a class of discrete SIR epidemic models which are derived from SIR epidemic models with distributed delays by using a variation of the backward Euler method.Applying a Lyapunov functional technique, it is shown that the global dynamics of each discrete SIR epidemic model are fully determined by a single threshold parameter and the effect of discrete time delays are harmless for the global stability of the endemic equilibrium of the model. |
| format | Article |
| id | doaj-art-56fa5225e82b4809861a1f4a004e34aa |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2010-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-56fa5225e82b4809861a1f4a004e34aa2025-01-24T02:00:28ZengAIMS PressMathematical Biosciences and Engineering1551-00182010-03-017234736110.3934/mbe.2010.7.347Global stability for a class of discrete SIR epidemic modelsYoichi Enatsu0Yukihiko Nakata1Yoshiaki Muroya2Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555In this paper, we propose a class of discrete SIR epidemic models which are derived from SIR epidemic models with distributed delays by using a variation of the backward Euler method.Applying a Lyapunov functional technique, it is shown that the global dynamics of each discrete SIR epidemic model are fully determined by a single threshold parameter and the effect of discrete time delays are harmless for the global stability of the endemic equilibrium of the model.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.347globally asymptotic stabilitydistributed delaysbackward euler methodlyapunov functional.discrete sir epidemic model |
| spellingShingle | Yoichi Enatsu Yukihiko Nakata Yoshiaki Muroya Global stability for a class of discrete SIR epidemic models Mathematical Biosciences and Engineering globally asymptotic stability distributed delays backward euler method lyapunov functional. discrete sir epidemic model |
| title | Global stability for a class of discrete SIR epidemic models |
| title_full | Global stability for a class of discrete SIR epidemic models |
| title_fullStr | Global stability for a class of discrete SIR epidemic models |
| title_full_unstemmed | Global stability for a class of discrete SIR epidemic models |
| title_short | Global stability for a class of discrete SIR epidemic models |
| title_sort | global stability for a class of discrete sir epidemic models |
| topic | globally asymptotic stability distributed delays backward euler method lyapunov functional. discrete sir epidemic model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.347 |
| work_keys_str_mv | AT yoichienatsu globalstabilityforaclassofdiscretesirepidemicmodels AT yukihikonakata globalstabilityforaclassofdiscretesirepidemicmodels AT yoshiakimuroya globalstabilityforaclassofdiscretesirepidemicmodels |