Mathematical models with computational simulations are useful tools for analyzing the spread and control of COVID-19 disease. In this study, we develop the previous models of COVID-19 pandemics. The vaccination compartment and its reaction rates are considered. Some key computational simulations and sensitivity analysis are applied on the model. Accordingly, three techniques of sensitivity analysis are discussed to compute the local sensitivities between model states and parameters. In addition, the basic reproduction number 𝑅0 is calculated for the model equilibrium points. The elasticity between the basic reproduction number, and the model parameters is also calculated. Furthermore, the daily real data of vaccinated cases in the United Kingdom from 15th March, 2021 to 31st December, 2021 are used. Results based on sensitivity analysis show that vaccination rate, contact tracing, rapid testing are the most important parameters to reduce the basic reproduction number. This helps international efforts to reduce the number of infected individuals from the disease. Another novelty in this work is that there is a good fit between the real data and model results. The model results will provide further control strategies and help local efforts to control this disease more effectively widely.