The COVID-19 outbreak, designated a “pandemic” by the World Health Organization (WHO) on 11 March 2020, has spread worldwide rapidly. Each country implemented prevention and control strategies, mainly classified as SARS LCS (SARS-like containment strategy) or PAIN LMS (pandemic influenza-like mitigation strategy). The reasons for variation in each strategy’s efficacy in controlling COVID-19 epidemics were unclear and are investigated in this paper. On the basis of the daily number of confirmed local (imported) cases and onset-to-confirmation distributions for local cases, we initially estimated the daily number of local (imported) illness onsets by a deconvolution method for mainland China, South Korea, Japan and Spain, and then estimated the effective reproduction numbers Rt by using a Bayesian method for each of the four countries. China and South Korea adopted a strict SARS LCS, to completely block the spread via lockdown, strict travel restrictions and by detection and isolation of patients, which led to persistent declines in effective reproduction numbers. In contrast, Japan and Spain adopted a typical PAIN LMS to mitigate the spread via maintaining social distance, self-quarantine and isolation etc., which reduced the Rt values but with oscillations around 1. The finding suggests that governments may need to consider multiple factors such as quantities of medical resources, the likely extent of the public’s compliance to different intensities of intervention measures, and the economic situation to design the most appropriate policies to fight COVID-19 epidemics.