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The COVID-19 Metro Manila curfew from 2020-03-15 to 2020-04-14 (8pm to 5am) does not prevent travelers from going to the airport (Ninoy Aquino International Airport, MNL) during the curfew hours.
However, it has been announced on 2020-03-16 evening a total lockdown, which is supposed to 1) lead to the cancellation of all outbound international flights departing MNL starting in around 72 hours. 2) might reduce/remove all taxi traffic? I'm not sure, I've heard conflicting information from people who are supposed to know (e.g., MNL information counter). It's a mess, I've given up trying to understand (I think nobody does), and announcements, including presidential addresses, code-mix three languages (English, Filipino, and some dialect).