A geometric analysis of the SIRS model with secondary infections
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929306763001856 |
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| author | Kaklamanos, Panagiotis Pugliese, Andrea Sensi, Mattia Sottile, Sara |
| author_facet | Kaklamanos, Panagiotis Pugliese, Andrea Sensi, Mattia Sottile, Sara |
| contents | We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria of the system and analyze their stability. We find conditions for the existence of two endemic equilibria, for some cases in which $\mathcal{R}_0 < 1$. Then, we unravel the interplay of the three time scales, providing conditions to foresee whether the system evolves in all three scales, or only in the fast and the intermediate ones. We conclude with numerical simulations and bifurcation analysis, to complement our analytical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03793 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A geometric analysis of the SIRS model with secondary infections Kaklamanos, Panagiotis Pugliese, Andrea Sensi, Mattia Sottile, Sara Dynamical Systems Physics and Society Populations and Evolution 34C23, 34C60, 34E13, 34E15, 37N25, 92D30 We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria of the system and analyze their stability. We find conditions for the existence of two endemic equilibria, for some cases in which $\mathcal{R}_0 < 1$. Then, we unravel the interplay of the three time scales, providing conditions to foresee whether the system evolves in all three scales, or only in the fast and the intermediate ones. We conclude with numerical simulations and bifurcation analysis, to complement our analytical results. |
| title | A geometric analysis of the SIRS model with secondary infections |
| topic | Dynamical Systems Physics and Society Populations and Evolution 34C23, 34C60, 34E13, 34E15, 37N25, 92D30 |
| url | https://arxiv.org/abs/2304.03793 |