The Impact of Random Noise on the Dynamics of COVID-19 Epidemic Model

Abstract

At the end of 2019, the world knew the propagation of a new pandemic named COVID-19. This disease harmed the exercises of humankind and changed our way of life. For modeling and studying infectious illness transmission, mathematical models are helpful tools. Thus, in this paper, taking into account the effect of the intensity of the noises, we define a threshold value Π s of the model, which determines the extinction and persistence of the COVID-19 pandemic. We give numerical simulations to illustrate the analytical results.

Nonlinear Stochastic SIS Epidemic Model Incorporating Lévy Process

“…Among the models proposed, the classic SIR epidemic model of Kermack and McKendrick is widely used [1] which divides the population into three classes, namely, susceptible (S), infected (I), and recovered (R). As a result, other works have generalized the Kermack-McKendrick (see, for example, [2][3][4][5][6][7][8]) model. On the other hand, for some diseases such as bacterial diseases and some sexually transmitted diseases, the SIR model is not suitable because the individuals infected with these diseases start to be susceptible, at a certain stage get the disease, and after a short infectious period become susceptible again [9,10].…”