  For a stochastic COVID-19 model with jump-diffusion, we prove the existence
and uniqueness of the global positive solution. We also investigate some
conditions for the extinction and persistence of the disease. We calculate the
threshold of the stochastic epidemic system which determines the extinction or
permanence of the disease at different intensities of the stochastic noises.
This threshold is denoted by $\xi$ which depends on the white and jump noises.
The effects of these noises on the dynamics of the model are studied. The
numerical experiments show that the random perturbation introduced in the
stochastic model suppresses disease outbreaks as compared to its deterministic
counterpart. In other words, the impact of the noises on the extinction and
persistence is high. When the noise is large or small, our numerical findings
show that the COVID-19 vanishes from the population if $\xi <1;$ whereas the
epidemic can't go out of control if $\xi >1.$ From this, we observe that white
noise and jump noise have a significant effect on the spread of COVID-19
infection, i.e., we can conclude that the stochastic model is more realistic
than the deterministic one. Finally, to illustrate this phenomenon, we put some
numerical simulations.
