Modeling the dynamics of the SARS-CoV-2 virus in a population with asymptomatic and symptomatic infected individuals and vaccination

The SARS-CoV-2 virus remains a pressing issue with unpredictable characteristics. The pandemic has spread worldwide through human interactions. Since the nature of the disease differs everywhere and it has a stochastic effect, we therefore develop a stochastic mathematical model to investigate its temporal dynamics. Asymptomatic individuals have a major effect on the spreading dynamics of the SARS-CoV-2 virus therefore, we divide the total population into susceptible, asymptomatic, symptomatic, and recovered groups. Multiple vaccinations have commenced across the globe. In this study, we assume that the vaccine confers permanent immunity. Moreover, due to the unpredictable characteristics of the disease random fluctuations are assumed in every population group. Using this model we show the existence and uniqueness of positive solutions to the proposed problem. We also discuss the disease extinction and persistence in the model to depict how contagious diseases can be eliminated from the community. We use the real data of SARS-CoV-2 virus, reported in Oman from the 1st January 2021 to 23rd May 2021 to parameterize the model. We then perform large-scale computational analysis to show the numerical simulation and verify the analytical findings.