BRUSSELS — The rapid spread of the new coronavirus presents a severe test for democracies, for the European Union as an institution and for the trans-Atlantic alliance.

And so far, it has been every nation for itself.

While Italy begged for aid, the European Union appeared to delay and fumble, with member states ignoring calls for solidarity. The United States, for its part, chose to try to cut itself off from Europe entirely.

President Trump’s decision to divide the United States from its European allies through a travel ban and blame them for inaction, rather than take a leadership role in cooperation and coordination, struck many analysts as particularly politicized and damaging, especially as European governments say the ban was imposed unilaterally, without consulting them.