The NYSE officials are adamant about the need for the exchange to remain open and to maintain a staff of flesh-and-blood traders on the floor even as the New York City Mayor Bill de Blasio hinted on Tuesday at the possibility of tighter restrictions on the movement of the city’s residents to mitigate the contagion, which has infected about 200,000 people world-wide and claimed nearly 8,000 lives, according to data compiled by Johns Hopkins University.