The current pandemic of COVID-19 caused tremendous effects on economic and social life all over the world in an unprecedentedly short period. Nonpharmaceutical measures such as city/country lockdown or stay at home orders have been applied in many countries until very recently. However, there is little systematic studies on the effects of such measures. We studied correlations among the timing of lockdown, reproduction number, total case number and deaths for 72 countries which had lockdown or similar policies as a social distancing intervention measure. We found a clear evidence for the effectiveness of the lockdown to reduce total case number and deaths. The result suggests that the cases number after the end of epidemic wave can be well predicted from the initial conditions at the lockdown for the most of 72 countries. On the other hand, several countries largely deviated from the prediction showed much slower decay in the daily cases number or even 2nd wave of epidemic after the lockdown. Possible reasons for the deviation from the prediction can be inferred from a mathematical modeling. We proposed a possible mechanism of these results both from a modified SIR model and the renewal equation approach. Strategy for the 2nd and 3 rd waves were discussed based on these models.