The stability of an SIR epidemic model with time delays
In this paper, an SIR epidemic model for the spread of an infectious disease transmitted by direct contact among humans and vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equili...
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| Format: | Article |
| Language: | English |
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AIMS Press
2005-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.101 |
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| _version_ | 1832590257316429824 |
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| author | Zhen Jin Zhien Ma |
| author_facet | Zhen Jin Zhien Ma |
| author_sort | Zhen Jin |
| collection | DOAJ |
| description | In this paper, an SIR epidemic model for the spread of an infectious disease transmitted by direct contact among humans and vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with respect to a ''weak delay''. Some known results are generalized. |
| format | Article |
| id | doaj-art-638aab85d1344782a2ab4318225251cf |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-638aab85d1344782a2ab4318225251cf2025-01-24T01:51:11ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-10-013110110910.3934/mbe.2006.3.101The stability of an SIR epidemic model with time delaysZhen Jin0Zhien Ma1Department of mathematics, North University of China, Taiyuan 030051, PRDepartment of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, PRIn this paper, an SIR epidemic model for the spread of an infectious disease transmitted by direct contact among humans and vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with respect to a ''weak delay''. Some known results are generalized.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.101global asymptotic stabilitytime delaylyapunov functional.sir epidemic model |
| spellingShingle | Zhen Jin Zhien Ma The stability of an SIR epidemic model with time delays Mathematical Biosciences and Engineering global asymptotic stability time delay lyapunov functional. sir epidemic model |
| title | The stability of an SIR epidemic model with time delays |
| title_full | The stability of an SIR epidemic model with time delays |
| title_fullStr | The stability of an SIR epidemic model with time delays |
| title_full_unstemmed | The stability of an SIR epidemic model with time delays |
| title_short | The stability of an SIR epidemic model with time delays |
| title_sort | stability of an sir epidemic model with time delays |
| topic | global asymptotic stability time delay lyapunov functional. sir epidemic model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.101 |
| work_keys_str_mv | AT zhenjin thestabilityofansirepidemicmodelwithtimedelays AT zhienma thestabilityofansirepidemicmodelwithtimedelays AT zhenjin stabilityofansirepidemicmodelwithtimedelays AT zhienma stabilityofansirepidemicmodelwithtimedelays |