Stochastic epidemic-type model with enhanced connectivity: exact solution

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.