My money is on DHS at this time.

At this moment there should be already a DHS crisis action team working 24/7 adjacent to the National Operations Center to coordinate all necessary information from all agencies/departments involved. CBP already has protocols in place, working with the the Public Health Service, to monitor border crossings at Ports of Entry and to take custody of anyone who is believed to be contagious. Coast Guard and CBP Air/Marine will activate existing plans for mass emigration along all waterways. CBP and ICE will patrol the rest of the border where illegal crossings occur to funnel as many as possible to intercept locations. Other support agencies (FEMA, various state/local agencies and other FedOps) will provide coordinated aid/services as necessary and determined by DHS. Throughout all of this effort there will be 4-a-day updates of all efforts/results to government senior leadership, and spot reports/decisions as required/appropriate.

Having just left that environment, I have my faith in the professionals who are on-the-job for just this type of headache. While this period of heightened alert is in effect, the "system" kicks into a higher gear. Overtime and special missions will occur, but the work will be done.