Stochastic delayed analysis of coronavirus model through efficient computational method.

Stochastic delayed modeling has a significant non-pharmaceutical intervention to control transmission dynamics of infectious diseases and its results are close to the reality of nature. The covid-19 has been controlled globally but there is still a threat and appears in different variants like omicron and SARS-CoV-2 etc. globally. This article, considered pattern a mathematical model based on Susceptible, Infected, and recovered populations with highly nonlinear incidence rates. we studied the dynamics of the coronavirus model; a newly proposed version is a stochastic delayed model that is based on nonlinear stochastic delayed differential equations (SDDEs). Transition probabilities and parametric perturbation methods were used for the construction of the stochastic delayed model. The fundamental properties like positivity, boundedness, existence and uniqueness, and stability results of equilibria of the model with certain conditions of reproduction number are studied regularly. Also, the extinction and persistence of disease are studied with the help of well-known theorems. The numerical methods used to find a visualization of results due to the complexity of stochastic delayed differential equations. Furthermore, for computational analysis, we implemented existing methods in the literature and compared their results with the proposed method like nonstandard finite difference for stochastic delayed model. The proposed method restores all dynamical properties of the model with a free choice of time steps.