Dynamic analysis of the recurrent epidemic model
In this work, an SIRS model with age structure is proposed for recurrent infectious disease by incorporating temporary immunity and delay. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the global stability of disease free equilibrium, the loca...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-06-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2019299?viewType=HTML |
| _version_ | 1811233938159435776 |
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| author | Hui Cao Dongxue Yan Ao Li |
| author_facet | Hui Cao Dongxue Yan Ao Li |
| author_sort | Hui Cao |
| collection | DOAJ |
| description | In this work, an SIRS model with age structure is proposed for recurrent infectious disease by incorporating temporary immunity and delay. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the global stability of disease free equilibrium, the local stability of endemic equilibrium, and the existence of Hopf bifurcation. Both non-periodic and periodic behaviors are possible when the disease persists in population, where time delay plays an important role. Numerical examples are provided to illustrate our theoretical results. |
| first_indexed | 2024-04-12T11:27:20Z |
| format | Article |
| id | doaj.art-3ff55a439e204b1f887340b73d19ae77 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-12T11:27:20Z |
| publishDate | 2019-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-3ff55a439e204b1f887340b73d19ae772022-12-22T03:35:09ZengAIMS PressMathematical Biosciences and Engineering1551-00182019-06-011655972599010.3934/mbe.2019299Dynamic analysis of the recurrent epidemic modelHui Cao0Dongxue Yan1Ao Li21. Department of Mathematics, Shaanxi University of Science and Technology, Xi’an, 710021, P.R. China2. School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, P.R. China3. Department of Applied Mathematics, The University of Western Ontario, London, N6A 5B7, CanadaIn this work, an SIRS model with age structure is proposed for recurrent infectious disease by incorporating temporary immunity and delay. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the global stability of disease free equilibrium, the local stability of endemic equilibrium, and the existence of Hopf bifurcation. Both non-periodic and periodic behaviors are possible when the disease persists in population, where time delay plays an important role. Numerical examples are provided to illustrate our theoretical results.https://www.aimspress.com/article/doi/10.3934/mbe.2019299?viewType=HTMLage-structured modelrecurrent epidemicc0-semigroupasymptotical stabilityhopf bifurcation |
| spellingShingle | Hui Cao Dongxue Yan Ao Li Dynamic analysis of the recurrent epidemic model Mathematical Biosciences and Engineering age-structured model recurrent epidemic c0-semigroup asymptotical stability hopf bifurcation |
| title | Dynamic analysis of the recurrent epidemic model |
| title_full | Dynamic analysis of the recurrent epidemic model |
| title_fullStr | Dynamic analysis of the recurrent epidemic model |
| title_full_unstemmed | Dynamic analysis of the recurrent epidemic model |
| title_short | Dynamic analysis of the recurrent epidemic model |
| title_sort | dynamic analysis of the recurrent epidemic model |
| topic | age-structured model recurrent epidemic c0-semigroup asymptotical stability hopf bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2019299?viewType=HTML |
| work_keys_str_mv | AT huicao dynamicanalysisoftherecurrentepidemicmodel AT dongxueyan dynamicanalysisoftherecurrentepidemicmodel AT aoli dynamicanalysisoftherecurrentepidemicmodel |