Coronavirus disease 2019 (COVID-19) has spread rapidly across the world. Tunisia reacted early to COVID-19, resulting in a low number of infections during the first wave of the pandemic. This study was performed to model the effects of different interventions on the evolution of cases and to compare these with the Tunisian experience. A stochastic transmission model was used to quantify the reduction in number of cases of COVID-19 with the interventions of contact tracing, compliance with isolation, and a general lockdown. In the model, increasing contact tracing from 20% to 80% after the first 100 cases reduced the cumulative number of infections (CNI) by 52% in 1 month. Similarly, increased compliance with isolation from 20% to 80% after the first 100 cases reduced the CNI by 45%. These reductions were smaller if the interventions were implemented after 1000 cases. A general lockdown reduced the CNI by 97% after the first 100 cases. Tunisia implemented its general lockdown after 75 cases were confirmed, which reduced the cumulative number of infected cases by 86% among the general population. This study shows that the early application of critical interventions contributes significantly to reducing infections and the evolution of COVID-19 in a country. Tunisia’s early success with the control of COVID-19 is explained by its quick response.