Dynamics of a Stochastic COVID-19 Epidemic Model with Jump-Diffusion

Tesfay, Almaz; Tesfay, Daniel; Khalaf, Anas; Brannan, James

For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution of the model. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of the epidemic system which determines the extinction or permanence of the disease at different intensities of the stochastic noises. This threshold is denoted by $\xi$ that depends on the white and jump noises. When the noise is large or small, our numerical findings show that the COVID-19 vanishes from the people if $\xi<1;$ whereas control the epidemic diseases if $\xi>1.$ From this, we observe that white noise and jump noise have a significant effect on the spread of COVID-19 infection. To illustrate this phenomenon, we put some numerical simulations.