The process of decision-making when dealing with infectious diseases is firmly based on mathematical modeling nowadays. One usual approach is to consider the adoption of compartmental methods such as SIR and SEIR and a large number of corresponding variations for modeling and prediction epidemic time series. Nevertheless, the COVID-19 epidemic characteristics and curves are apparently challenging the results obtained by these models. This chapter presents the results of two traditional compartmental models, SIR (Susceptible—Infected–Recovered) and SEIR (Susceptible–Exposed–Infected–Recovered), and an adapted version of the SEIR, called SEIR with Intervention, which captures the impact of containment measures for the dynamics of the infection rate. The analysis is performed for five countries: China, United States, Brazil, Italy, and Singapore, each of them with specific characteristics of dealing with the pandemic. A sequence of results is presented, considering different parameters, in order to understand the feasibility of application for each model.