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<p>We propose a new dynamic SIR model that, in contrast with the available model on time scales, is biological relevant. For the new SIR model we obtain an explicit solution, we prove the asymptotic stability of the extinction and disease-free equilibria, and deduce some necessary conditions for the monotonic behavior of the infected population. The new results are illustrated with several examples in the discrete, continuous, and quantum settings.</p>

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A consistent SIR model on time scales with exact solution

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年9月15日

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  • Márcia Lemos-Silva,
  • Sandra Vaz,
  • Delfim F. M. Torres

摘要

We propose a new dynamic SIR model that, in contrast with the available model on time scales, is biological relevant. For the new SIR model we obtain an explicit solution, we prove the asymptotic stability of the extinction and disease-free equilibria, and deduce some necessary conditions for the monotonic behavior of the infected population. The new results are illustrated with several examples in the discrete, continuous, and quantum settings.