The dawn of corona virus (COVID-19) has become a worldwide matter of concern. Some mathematical modeling has been developed to comprehend the spread of the virus and inhibit the virus infection. In order to make predictions, develop control strategies, and assess them, it is essential to have a better understanding of the transmission mechanism and the undermining elements of the spread of infectious diseases. Practically, mathematical modeling is a way for evaluating epidemics and the effects of various assumptions made about potential treatments. This study intends to acquire a more accurate mathematical model dynamics of the disease using computational modeling and compare it to the current model. This research incorporates a new trajectory in the study of COVID-19. The newly proposed model integrates quarantined and vaccinated data which has not been studied so far in my understanding. We derive the numerical approximations of the model equations employing computational modeling. As a result, the estimated parameters and initial population model states have different model dynamics. The findings in this analysis mark a significant advancement in the ability to forecast model dynamics for development capacities, interventions, and healthcare methodologies.