Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate
The periodic oscillation transmission of infectious diseases is widespread, deep understanding of this periodic pattern and exploring the generation mechanism, and identifying the specific factors that lead to such periodic outbreaks, which are of very importanceto predict and control the spread of...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2024/5373794 |
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| _version_ | 1832546210778447872 |
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| author | Yingying Zhang Ruohan Wang Yanan Cai |
| author_facet | Yingying Zhang Ruohan Wang Yanan Cai |
| author_sort | Yingying Zhang |
| collection | DOAJ |
| description | The periodic oscillation transmission of infectious diseases is widespread, deep understanding of this periodic pattern and exploring the generation mechanism, and identifying the specific factors that lead to such periodic outbreaks, which are of very importanceto predict and control the spread of infectious diseases. In this study, to further reveal the mathematical mechanism of spontaneous generation of periodic oscillation solution, we investigate a type of SEIR epidemic model with a small intrinsic growth rate. By utilizing the singular perturbation theory and center manifold theorem, we extend the relaxation oscillation of three-dimensional SIR models to the four-dimensional SEIR models and prove the existence of stable relaxation oscillation with a large amplitude in the model. Numerical simulations are performed to verify our theoretical results. The results presented in this study provide a new idea for the study of the intrinsic mechanism of periodic oscillation in epidemiology, enrich the dynamics of epidemic models, and deepen the understanding of the global dynamics of these models. |
| format | Article |
| id | doaj-art-936bcc406292471796bdd798595f12ad |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-936bcc406292471796bdd798595f12ad2025-02-03T07:23:32ZengWileyComplexity1099-05262024-01-01202410.1155/2024/5373794Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth RateYingying Zhang0Ruohan Wang1Yanan Cai2College of ScienceSchool of Mathematics and PhysicsCollege of ScienceThe periodic oscillation transmission of infectious diseases is widespread, deep understanding of this periodic pattern and exploring the generation mechanism, and identifying the specific factors that lead to such periodic outbreaks, which are of very importanceto predict and control the spread of infectious diseases. In this study, to further reveal the mathematical mechanism of spontaneous generation of periodic oscillation solution, we investigate a type of SEIR epidemic model with a small intrinsic growth rate. By utilizing the singular perturbation theory and center manifold theorem, we extend the relaxation oscillation of three-dimensional SIR models to the four-dimensional SEIR models and prove the existence of stable relaxation oscillation with a large amplitude in the model. Numerical simulations are performed to verify our theoretical results. The results presented in this study provide a new idea for the study of the intrinsic mechanism of periodic oscillation in epidemiology, enrich the dynamics of epidemic models, and deepen the understanding of the global dynamics of these models.http://dx.doi.org/10.1155/2024/5373794 |
| spellingShingle | Yingying Zhang Ruohan Wang Yanan Cai Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate Complexity |
| title | Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate |
| title_full | Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate |
| title_fullStr | Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate |
| title_full_unstemmed | Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate |
| title_short | Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate |
| title_sort | relaxation oscillation in seir epidemic models with the intrinsic growth rate |
| url | http://dx.doi.org/10.1155/2024/5373794 |
| work_keys_str_mv | AT yingyingzhang relaxationoscillationinseirepidemicmodelswiththeintrinsicgrowthrate AT ruohanwang relaxationoscillationinseirepidemicmodelswiththeintrinsicgrowthrate AT yanancai relaxationoscillationinseirepidemicmodelswiththeintrinsicgrowthrate |