Rorate Caeli

Cancelling Masses to stop an epidemic?

Both secular and Catholic news media are now full of reports (such as this) that, in response to the swine flu epidemic, the Archdiocese of Mexico had cancelled Masses without exception last Sunday, April 26. Apparently, churches in Mexico City remain closed up to now.
This is deeply disturbing. Our prayers and sympathies are with the people of Mexico as they come to grips with this terrible scourge. However, should we not ask out loud: is this the way to combat disease: by preventing the faithful from attending Holy Mass?
This does seem odd in a country where, only in the last century, people risked torture and martyrdom in order to attend clandestine Masses! Are we missing something?