A model to study the formation of compositional patterns in concentrated binary alloys under irradiation is presented. In this model, six atomic and defect species are considered: regular lattice atoms (A and B), dumbbell interstitials (AA, BB and AB) and vacancies. In addition to long range diffusion of these species, local defect-defect (vacancy-interstitial recombination) and defect-atom (dumbbell-atom) reactions have also been considered. The model tracks simultaneous evolution of all the species in reaction-diffusion formalism. Irradiation events are modeled as a stochastic point process which changes the concentration of all the species instantaneously in a random fashion. In each irradiation event, a spatial distribution of point defects (core-shell distribution: core dominated by vacancies and shell by interstitials) has been introduced in the system which drives the kinetics of diffusion and reaction. The model has been non-dimensionalized with respect to intrinsic length and time scales of the material system and solved numerically using finite difference technique. Applying this model to CuAu solid solution, we have shown that the alloy exhibits spinodal-like decomposition with specific steady state wavelengths that depend on the irradiation conditions.