Analysis of the Diffusion SIR Epidemic Model With Networked Delay and Nonlinear Incidence Rate
This paper is concerned with the qualitative analysis of a diffusion SIR epidemic model with networked delay and nonlinear incidence rate. First, we prove the existence and uniqueness of the model by using the method of upper and lower solutions. Then, we prove that the trivial equilibrium (0, 0) is...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/5739758 |
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| _version_ | 1832557994300145664 |
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| author | Xiangyu Tang Yujuan Chen |
| author_facet | Xiangyu Tang Yujuan Chen |
| author_sort | Xiangyu Tang |
| collection | DOAJ |
| description | This paper is concerned with the qualitative analysis of a diffusion SIR epidemic model with networked delay and nonlinear incidence rate. First, we prove the existence and uniqueness of the model by using the method of upper and lower solutions. Then, we prove that the trivial equilibrium (0, 0) is unstable; the disease-free equilibrium (N, 0) is locally asymptotically stable if the reproduction number R0≤1 and unstable if R0>1; the endemic equilibrium S∗,I∗ is locally asymptotically stable if R0≤R1 or if R1<R0 and τ<τ10∗; and S∗,I∗ is unstable if R1<R0 and τ>τ10∗. Moreover, when R1<R0, we show that hopf bifurcation occurs at S∗,I∗ and τ=τ10∗. Numerical results are provided for theoretical discoveries. |
| format | Article |
| id | doaj-art-c6921f43660046cb9c9571213f84538f |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c6921f43660046cb9c9571213f84538f2025-02-03T01:45:32ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/5739758Analysis of the Diffusion SIR Epidemic Model With Networked Delay and Nonlinear Incidence RateXiangyu Tang0Yujuan Chen1School of Mathematics and StatisticsSchool of Mathematics and StatisticsThis paper is concerned with the qualitative analysis of a diffusion SIR epidemic model with networked delay and nonlinear incidence rate. First, we prove the existence and uniqueness of the model by using the method of upper and lower solutions. Then, we prove that the trivial equilibrium (0, 0) is unstable; the disease-free equilibrium (N, 0) is locally asymptotically stable if the reproduction number R0≤1 and unstable if R0>1; the endemic equilibrium S∗,I∗ is locally asymptotically stable if R0≤R1 or if R1<R0 and τ<τ10∗; and S∗,I∗ is unstable if R1<R0 and τ>τ10∗. Moreover, when R1<R0, we show that hopf bifurcation occurs at S∗,I∗ and τ=τ10∗. Numerical results are provided for theoretical discoveries.http://dx.doi.org/10.1155/2024/5739758 |
| spellingShingle | Xiangyu Tang Yujuan Chen Analysis of the Diffusion SIR Epidemic Model With Networked Delay and Nonlinear Incidence Rate Journal of Mathematics |
| title | Analysis of the Diffusion SIR Epidemic Model With Networked Delay and Nonlinear Incidence Rate |
| title_full | Analysis of the Diffusion SIR Epidemic Model With Networked Delay and Nonlinear Incidence Rate |
| title_fullStr | Analysis of the Diffusion SIR Epidemic Model With Networked Delay and Nonlinear Incidence Rate |
| title_full_unstemmed | Analysis of the Diffusion SIR Epidemic Model With Networked Delay and Nonlinear Incidence Rate |
| title_short | Analysis of the Diffusion SIR Epidemic Model With Networked Delay and Nonlinear Incidence Rate |
| title_sort | analysis of the diffusion sir epidemic model with networked delay and nonlinear incidence rate |
| url | http://dx.doi.org/10.1155/2024/5739758 |
| work_keys_str_mv | AT xiangyutang analysisofthediffusionsirepidemicmodelwithnetworkeddelayandnonlinearincidencerate AT yujuanchen analysisofthediffusionsirepidemicmodelwithnetworkeddelayandnonlinearincidencerate |