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Mathematics > Dynamical Systems

arXiv:2503.03540 (math)
[Submitted on 5 Mar 2025]

Title:An SIRS model with hospitalizations: economic impact by disease severity

Authors:Jacopo Borsotti
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Abstract:We introduce a two-timescale SIRS-type model in which a fraction $\theta$ 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 $\theta$ that maximizes the total number of hospitalized individuals for long times, revealing that this optimal 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 $\theta$ of infected individuals develops symptoms and self-quarantines.
Subjects: Dynamical Systems (math.DS); Populations and Evolution (q-bio.PE)
Cite as: arXiv:2503.03540 [math.DS]
  (or arXiv:2503.03540v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.2503.03540

Submission history

From: Jacopo Borsotti [view email]
[v1] Wed, 5 Mar 2025 14:25:46 UTC (2,126 KB)
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