Senior Trump administration officials discussed shutting down travel from Italy and South Korea as the coronavirus outbreak worsened in those countries, but ultimately decided the virus is spreading too quickly to be contained, sources with direct knowledge of the discussions tell Axios.

Why it matters: It's extremely difficult to contain a viral outbreak in a globalized society, and if such a strategy isn't likely to be much help, it's even harder to justify the diplomatic, logistical and economic consequences.

What we're hearing: Several federal agencies, including the State and Defense departments, were concerned about cutting off travel from those countries because the U.S. has a strong military presence in South Korea and Italy's central location in the European Union would complicate restrictions, the sources said.

Public health officials involved in the talks also tended to not favor travel bans, which informed the ultimate decision not to restrict travel from Italy and South Korea, one of the sources said.

"You want to move towards mitigating, knowing that once you figure out that the virus is spreading consistently across America or in certain spots, there's diminishing returns," the source said.

While curtailing travel to China was viewed as having a high return in the early days of the outbreak, the same wasn't true of Italy and South Korea — especially because the virus is spreading through other European countries beyond Italy, the source added.

Vice President Mike Pence's chief of staff Marc Short told Axios he wouldn't "comment specifically on conversations we have inside the WH Situation Room and disappointed other[s] do, but the purpose of the task force in part is to allow discussion around many points of view to try to reach the best recommendation possible to deliver to the President. Many viewpoints are represented every day."

What's next: Trump has just arrived on Capitol Hill to discuss options for combatting the economic effects of the coronavirus with Senate Republicans. Pence, Treasury Secretary Steven Mnuchin, National Economic Council director Larry Kudlow, and trade adviser Peter Navarro are also attending the meeting.