Abstarct: Abstract In this thesis, various models including SEIR and SEIUR with piecewise and optimal control approaches have been employed to simulate the COVID-19 pandemic. Using real from the United States, Sri Lanka, Ireland, China, and South Korea, key parameters such as transmission rate, removal rate, and basic reproduction number were estimated. In the SEIUR model, a new compartment for unreported infected individuals was introduced to overcome the limitation of classical models. Furthermore, time-varying parameters were used instead of constant parameters, along with piecewise modeling in which time intervals are divided baxsed on the timing of health policy implementation and government interventions. The results indicate that dynamic models with time-varying parameters significantly enhance prediction accuracy, such that the error of the piecewise SEIUR model in predicting US data is less than 5%, and its coefficient of determination R^2 is close to 1. Furthermore, a comparison of control strategies reveals that the suppression approach (implementing maximum interventions from the outset) is not only more effective but also less economically costly than mitigation (gradual control), but also imposes lower economic costs and prevents the collapse of the healthcare system. In the optimal control model for Ireland, it was found that rapid and intense implementation of non-pharmaceutical interventions substantially reduces the number of deaths and shortens the period of stringent restrictions. These studies outline the evolution of epidemic models from classical and static forms toward flexible, piecewise, and data-driven structures, and demonstrate that combining mathematical modeling with real data and optimal control can lead to better decision-making in managing health crises.