A geometric analysis of the SIRS model with secondary infections

Fuente: arXiv
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Auteurs principaux: Kaklamanos, Panagiotis, Pugliese, Andrea, Sensi, Mattia, Sottile, Sara
Format: Preprint
Publié: 2023
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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