An SIRS model with hospitalizations: economic impact by disease severity
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913979043938304 |
|---|---|
| author | Borsotti, Jacopo |
| author_facet | Borsotti, Jacopo |
| contents | We introduce a two-timescale SIRS-type model in which a fraction $θ$ of infected individuals experiences a severe course of the disease, requiring hospitalization. During hospitalization, these individuals do not contribute to further infections. We analyze the model's equilibria, perform a bifurcation analysis, and explore its two-timescale nature (using techniques from Geometric Singular Perturbation Theory). Our main result provides an explicit expression for the value of $θ$ that maximizes the total number of hospitalized individuals for long times, revealing that this fraction can be lower than 1. This highlights the interesting effect that a severe disease, by necessitating widespread hospitalization, can indirectly suppress contagions and, consequently, reduce hospitalizations. Numerical simulations illustrate the growth in the number of hospitalizations for short times. The model can also be interpreted as a scenario where only a fraction $θ$ of infected individuals develops symptoms and self-quarantines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03540 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An SIRS model with hospitalizations: economic impact by disease severity Borsotti, Jacopo Dynamical Systems Populations and Evolution 34E13, 37N25 (Primary) 92D30, 34C45 (Secondary) We introduce a two-timescale SIRS-type model in which a fraction $θ$ of infected individuals experiences a severe course of the disease, requiring hospitalization. During hospitalization, these individuals do not contribute to further infections. We analyze the model's equilibria, perform a bifurcation analysis, and explore its two-timescale nature (using techniques from Geometric Singular Perturbation Theory). Our main result provides an explicit expression for the value of $θ$ that maximizes the total number of hospitalized individuals for long times, revealing that this fraction can be lower than 1. This highlights the interesting effect that a severe disease, by necessitating widespread hospitalization, can indirectly suppress contagions and, consequently, reduce hospitalizations. Numerical simulations illustrate the growth in the number of hospitalizations for short times. The model can also be interpreted as a scenario where only a fraction $θ$ of infected individuals develops symptoms and self-quarantines. |
| title | An SIRS model with hospitalizations: economic impact by disease severity |
| topic | Dynamical Systems Populations and Evolution 34E13, 37N25 (Primary) 92D30, 34C45 (Secondary) |
| url | https://arxiv.org/abs/2503.03540 |