Exact solution for a quantum SIR model
Abstract
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.
Keywords
Cite
@article{arxiv.2512.09951,
title = {Exact solution for a quantum SIR model},
author = {Márcia Lemos-Silva and Sandra Vaz and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:2512.09951},
year = {2026}
}
Comments
This is a preprint of a paper published in 'Journal of Mathematical Sciences' at [https://doi.org/10.1007/s10958-025-08181-6]