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<p>Based on the classical continuous system initially proposed by Bailey in 1975, we present a novel Susceptible–Infected–Removed (SIR) model defined in quantum time, where the temporal evolution is governed by a non-uniform time grid. An explicit analytical solution is derived, and the long-term behavior of the susceptible, infected, and removed individuals is analyzed. Moreover, we prove the model preserves dynamic consistency with its continuous counterpart, as evidenced by the non-negativity of solutions and their corresponding qualitative agreement with the continuous dynamics. All results are further supported by illustrative examples.</p>

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EXACT SOLUTION FOR A QUANTUM SIR MODEL

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月16日

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

摘要

Based on the classical continuous system initially proposed by Bailey in 1975, we present a novel Susceptible–Infected–Removed (SIR) model defined in quantum time, where the temporal evolution is governed by a non-uniform time grid. An explicit analytical solution is derived, and the long-term behavior of the susceptible, infected, and removed individuals is analyzed. Moreover, we prove the model preserves dynamic consistency with its continuous counterpart, as evidenced by the non-negativity of solutions and their corresponding qualitative agreement with the continuous dynamics. All results are further supported by illustrative examples.