  Natural fluctuations have played a crucial role in affecting the dynamics of
pervasive diseases such as the coronavirus. Examining the effects of irregular
unsettling disturbances on epidemic models is important for understanding these
dynamics. In this study, we introduce a mathematical model for the SIR
(Susceptible-Infectious-Recovered) dynamics of the coronavirus, incorporating
perturbations in the contact rate through Levy noise. The utilization of the
Levy process is essential for the protection and control of diseases. We delve
into the dynamics of both the deterministic model and the global positive
solution of the stochastic model, establishing their existence and uniqueness.
Additionally, we explore conditions for the termination and persistence of the
infection. Furthermore, we derive the basic reproduction number, a critical
determinant of disease extinction or persistence. Numerical results indicate
that COVID-19 dissipates from the population when the reproduction number is
less than one in the presence of significant or minor noise. Conversely,
controlling epidemic diseases becomes challenging when the reproduction number
exceeds one. To illustrate this phenomenon, we provide numerical simulations,
offering insights into the dynamics of the disease and the efficacy of control
measures
