A stochastic SIRS epidemic model with generalized nonlinear incidence and Levy noise is investigated. First, we show the existence and uniqueness of a global positive solution. Then, we establish sufficient conditions for the extinction and persistence of the disease. The main results are proved under weak assumptions regarding the incidence function, the obtained results are proved under a Levy-type perturbation without requiring the finiteness of its activity. Finally, numerical simulations are realized to illustrate the main results.(c) 2023 Elsevier B.V. All rights reserved.