The transcritical Bogdanov Takens bifurcation with boundary due to the risk perception on a recruitment epidemiological model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917618985730048 |
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| author | Castro-Echeverría, Jocelyn A. Verduzco, Fernando Velasco-Hernández, Jorge X. |
| author_facet | Castro-Echeverría, Jocelyn A. Verduzco, Fernando Velasco-Hernández, Jorge X. |
| contents | We analyze an epidemiological model with treatment and recruitment considering the risk perception. In this model, we consider an exponential function as a recruitment rate. We have found that this model undergoes the transcritical Bogdanov-Takens bifurcation with boundary, where the system experiences the transcritical bifurcation between the disease-free equilibrium point and the endemic equilibrium point. The Hopf bifurcation also arises at the endemic equilibrium point, this is, the appearance or disappearance of a limit cycle, and finally, the Homoclinic bifurcation which transforms the limit cycle into a homoclinic cycle, starting and ending at the disease-free equilibrium point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The transcritical Bogdanov Takens bifurcation with boundary due to the risk perception on a recruitment epidemiological model Castro-Echeverría, Jocelyn A. Verduzco, Fernando Velasco-Hernández, Jorge X. Dynamical Systems We analyze an epidemiological model with treatment and recruitment considering the risk perception. In this model, we consider an exponential function as a recruitment rate. We have found that this model undergoes the transcritical Bogdanov-Takens bifurcation with boundary, where the system experiences the transcritical bifurcation between the disease-free equilibrium point and the endemic equilibrium point. The Hopf bifurcation also arises at the endemic equilibrium point, this is, the appearance or disappearance of a limit cycle, and finally, the Homoclinic bifurcation which transforms the limit cycle into a homoclinic cycle, starting and ending at the disease-free equilibrium point. |
| title | The transcritical Bogdanov Takens bifurcation with boundary due to the risk perception on a recruitment epidemiological model |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2403.14147 |