Ooh, this could be fun, Trekify The Last Ship. The Nebula class USS Nathan James is all that remains of Starfleet after a devastating plague has crippled most of the Alpha Quadrant. Avoiding outbreak by being in the Beta Quadrant out of comms-range, supposedly to test out new equipment, it turns out this mission was a ruse for visiting Vulcan scientist Dr. T'Scott trying to find a cure.
There's also a Romulan Warbird out there trying to stop the Nathan James from finding a cure so they can develop a cure and control it themselves.
The Alpha Quadrant, and presumably Earth devastated by a plague. Sounds like quite the Crusade they'd be undertaking.