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 ξ which depends on 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 outbreak 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 COVID-19 vanishes from the population if \(\xi <1\); whereas the epidemic cannot 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.

对于具有跳跃扩散的随机COVID-19模型，我们证明了全局正解的存在性和唯一性。我们还调查了该疾病的灭绝和持续性的一些情况。我们计算了随机流行系统的阈值，该阈值确定了在不同强度的随机噪声下该疾病的灭绝或持久性。该阈值由ξ表示这取决于白噪声和跳跃噪声。研究了这些噪声对模型动力学的影响。数值实验表明，与确定性模型相比，随机模型中引入的随机扰动抑制了疾病的爆发。换句话说，噪声对消光和持久性的影响很大。当噪声较大或较小时，我们的数值发现表明，如果\（\ xi <1 \），则COVID-19会从总体中消失。如果\（\ xi> 1 \），则该流行病不会失控。据此，我们观察到白噪声和跳跃噪声对COVID-19感染的传播具有显着影响，即，我们可以得出结论，随机模型比确定性模型更现实。最后，为了说明这种现象，我们进行了一些数值模拟。