Stochastic Analysis of COVID-19 Epidemic Model

Abstract

In our work, we focused on examining the epidemic transmission dynamics of the  stochastic model for COVID-19. We prove the existence and uniqueness of a global positive solution which allowed us to better understand the underlying mechanisms of disease spread and explore the concepts of disease extinction and persistence within the stochastic model.  By identifying key parameters and variables, we were able to determine potential scenarios in which the disease could die out naturally over time, as well as situations where it could persist in a sustainable manner within the population studied. We also carried out numerical simulations which allowed us to validate our theoretical results and visualize in a concrete way how the parameters of the model affect the dynamics of the disease.  By analyzing these simulations, we were able to identify patterns of spread and assess the conditions under which a disease might disappear or persist in the study population.