The coronavirus disease 2019 (COVID-19) has become a life-threatening pandemic. The epidemic trends in different countries vary considerably due to different policy-making and resources mobilization. We calculated basic reproduction number (R₀) and the time-varying estimate of the effective reproductive number (R_t) of COVID-19 by using the maximum likelihood method and the sequential Bayesian method, respectively. European and North American countries possessed higher R₀ and unsteady R_t fluctuations, whereas some heavily affected Asian countries showed relatively low R₀ and declining R_t now. The numbers of patients in Africa and Latin America are still low, but the potential risk of huge outbreaks cannot be ignored. Three scenarios were then simulated, generating distinct outcomes by using SEIR (susceptible, exposed, infectious, and removed) model. First, evidence-based prompt responses yield lower transmission rate followed by decreasing R_t. Second, implementation of effective control policies at a relatively late stage, in spite of huge casualties at early phase, can still achieve containment and mitigation. Third, wisely taking advantage of the time-window for developing countries in Africa and Latin America to adopt adequate measures can save more people’s life. Our mathematical modeling provides evidence for international communities to develop sound design of containment and mitigation policies for COVID-19.