Stochastic epidemic-type model with enhanced connectivity: exact solution

TL;DR

This paper introduces an exact analytical solution for a one-dimensional SIR epidemic model with connectivity-dependent infection rates, using a quantum spin approach, enabling precise calculation of epidemic dynamics.

Contribution

It provides the first exact solution for a 1D SIR model with neighbor-dependent infection rates using a quantum mechanical framework.

Findings

Exact time-dependent densities for S, I, R populations

Validation against previous low connectivity SIR models

Exact solutions for correlation functions

Abstract

We present an exact analytical solution to a one-dimensional model of the Susceptible-Infected-Recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming the master equation via a quantum spin operator formulation. We calculate exactly the time-dependent density of infected, recovered and susceptible populations for random initial conditions, and compare our results with a low connectivity SIR model reported by Schuetz et al.. Our results compare well to those of previous work, validating the model as a useful tool for additional and extended studies in this important area. Our model also provides exact solutions for the n-point correlation functions, and can be extended to more complex epidemic type models.