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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.09951 |
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| _version_ | 1866911371144200192 |
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| author | Lemos-Silva, Márcia Vaz, Sandra Torres, Delfim F. M. |
| author_facet | Lemos-Silva, Márcia Vaz, Sandra Torres, Delfim F. M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact solution for a quantum SIR model Lemos-Silva, Márcia Vaz, Sandra Torres, Delfim F. M. Dynamical Systems 81Q80, 92D30 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. |
| title | Exact solution for a quantum SIR model |
| topic | Dynamical Systems 81Q80, 92D30 |
| url | https://arxiv.org/abs/2512.09951 |