  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.
