Before revision:  Numerical simulations on different L\'evy disturbances are carried out to verify the obtained theoretical results .
After revision:  One of the most interesting results is that the dynamics of the stochastic model are closely related to the intensities of white noises and L'evy jumps, which can give us a good insight into the evolution of the epidemic in some unexpected situations. Our work complements the results of some previous investigations and provides a new approach to predict and analyze the dynamic behavior of epidemics with distributed delay. For illustrative purposes, numerical examples are presented for checking the theoretical study