Before revision: In this article, taking into account distributed delay and multidimensional L\'evy disturbances, wepresent an exhaustive study on the dynamic of the Susceptible-Infected-Removed (SIR ) model .
After revision: Recently, emerging epidemics like COVID-19 and its variants require predictive mathematical models to implement suitable responses in order to limit their negative and profound impact on society. The SIR (Susceptible-InfectedRemoved) system is a straightforward mathematical formulation to model the dissemination of many infectious diseases. The present paper reports novel theoretical and analytical results for a perturbed version of an SIR model with Gamma-distributed delay. Notably, our epidemic model is represented by It\^o-L'evy stochastic differential equations in order to simulate sudden and unexpected external phenomena. By using some new and ameliorated mathematical approaches, we study the dynamic of the Susceptible-Infected-Removed (SIR ) model .