The outbreak of COVID-19 disease caused by the SARS-CoV-2 in 2019 has claimed over 6.3 million lives. The pandemic prompted many countries to set up some preventive measures as means to control the spread of the disease. In this thesis, a deterministic system of coupled differential equations is proposed to study the transmission of COVID-19 among a well-mixed population with intervention strategies. The existence and uniqueness of the classical solution of the COVID-19 model are proved. The equilibrium points of the model are analyzed and, the basic reproduction number is obtained. The local asymptotic stability and the global asymptotic stability of the model are carried out. An adaptive Dormand\textendash Prince numerical method is used to obtain approximate solution of the model. The results shows that combined control parameters may reduce the burden of COVID-19 faster in the population. In addition, the outcomes of this study show that in order to mitigate the spread of COVID-19 in the overall population, non-pharmaceutical intervention strategies such as social distancing, self-isolation, and hand washing should be practiced at the maximum and people should be vaccinated.