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.

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We present the prevention of influenza pandemic by using multiple control functions. First, we adjust the control functions in the pandemic model, then we show the existence of the optimal control problem, and, by using both analytical and numerical techniques, we investigate cost-effective control effects for the prevention of transmission of disease. To do this, we use four control functions, the first one for increasing the effect of vaccination, the second one for the strategies to isolate infected individuals, and the last two for the antiviral treatment to control clinically infectious and hospitalization cases, respectively. We completely characterized the optimal control and compute the numerical solution of the optimality system by using an iterative method.

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We present the prevention of avian influenza pandemic by adjusting multiple control functions in the human-to-human transmittable avian influenza model. First we show the existence of the optimal control problem; then by using both analytical and numerical techniques, we investigate the cost-effective control effects for the prevention of transmission of disease. To do this, we use three control functions, the effort to reduce the number of contacts with human infected with mutant avian influenza, the antiviral treatment of infected individuals, and the effort to reduce the number of infected birds. We completely characterized the optimal control and compute numerical solution of the optimality system by using an iterative method.