Exact solution for a quantum SIR model

TL;DR

This paper introduces a quantum time-based SIR model, providing an explicit analytical solution and demonstrating its consistency with classical models through theoretical analysis and illustrative examples.

Contribution

It presents the first exact analytical solution for a quantum SIR model with non-uniform time evolution, extending classical epidemiological modeling into quantum dynamics.

Findings

Explicit analytical solution derived

Model preserves dynamic consistency with classical SIR

Solutions maintain non-negativity and qualitative agreement

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.