  We solve an one-dimensional stochastic model of interacting particles on a
chain. Particles can have branching and coagulation reactions, they can also
appear on an empty site and disappear spontaneously.
  This model which can be viewed as an epidemic model and/or as a
generalization of the {\it voter} model, is treated analytically beyond the
{\it conventional} solvable situations. With help of a suitably chosen {\it
string function}, which is simply related to the density and the
non-instantaneous two-point correlation functions of the particles, exact
expressions of the density and of the non-instantaneous two-point correlation
functions, as well as the relaxation spectrum are obtained on a finite and
periodic lattice.
