Solutions generated through numerical techniques are great in solving real-world problems. This manuscript deals with the numerical approximation of the epidemic system, describing the transmission dynamics of the Vercilla Zoster Virus (VZV) through the impact of vaccination. To discretize the continuous dynamical system, we proposed a novel numerical technique that preserves the true dynamics of the VZV epidemic model. The proposed technique is established in such a manner that it sustains all necessary physical traits depicted by the epidemic model under study. The designed technique is named a nonstandard finite difference (NSFD) scheme. Theoretical analysis of the designed NSFD technique is presented which describes its strength over the standard numerical procedures which are already being used for such purposes. The graphical solutions of all the numerical techniques are presented which verify the efficacy of the proposed NSFDS technique.