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Employing running QCD renormalization group parameters α s (μ) and m s (μ) we obtain strangeness production yields in the deconfined quark-gluon plasma (QGP) phase. We model a dynamically evolving QGP fireball as could be formed in relativistic nuclear collisions and obtain the total strangeness per baryon yield as function of energy and impact parameter. We also study strangeness phase space occupancy varying the hadronization and freeze-out conditions of the expanding QGP fireball.