You are absolutely right - a number of airlines did cancel flights. But others did not. And all legitimate airlines accepted the responsibility of rerouting passengers from cancelled flights onto other airlines so their passengers were not stranded. For eg, South African airways (I was in Jo'berg) told me they would have rerouted me on BA to London and then BA to Cairo (BA were still flying into Cairo). Because Ethiopian accepted no such responsibility to reroute, I had to book an expensive one way fare from Jo'berg to Cairo on Qatar (via Doha) - and still got no satisfaction from Ethiopian on the ticket refund!
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