Stationary distribution and long-time behavior of COVID-19 model with stochastic effect

Abstract

The coronavirus disease (COVID-19) is a dangerous pandemic and it spreads to many people in most of the world. In this paper, we propose a COVID-19 model with the assumption that it is affected by randomness. For positivity, we prove the global existence of positive solution and the system exhibits extinction under certain parametric restrictions. Moreover, we establish the stability region for the stochastic model under the behavior of stationary distribution. The stationary distribution gives the guarantee of the appearance of infection in the population. Besides that, we find the reproduction ratio [Formula: see text] for prevail and disappear of infection within the human population. From the graphical representation, we have validated the threshold conditions that define in our theoretical findings.