SAN DIEGO -- Padres infielder Jorge Mateo tested positive for the coronavirus upon his intake screening, manager Jayce Tingler announced on Wednesday. Mateo has experienced some symptoms of the virus, including the loss of taste and smell, and he is currently self-isolating.

Tingler noted that Mateo’s symptoms have recently begun to improve. The announcement from the Padres' manager means Mateo gave the team permission to divulge his diagnosis.

The Padres traded for Mateo a week ago in Major League Baseball's first trade since the roster freeze was lifted. San Diego sent a player to be named later or cash to Oakland in return for Mateo, a speedy middle infielder who projected as a useful utility man on the Padres' roster.

Mateo joins Tommy Pham as the Padres who have tested positive for the coronavirus. Both of those positive tests came upon intake screening, meaning neither of the two has been in contact with other members of the team. Pham remains asymptomatic, Tingler said.

It'd be unfair to speculate on Mateo's potential return. But he was out of options and a near certainty to make the Opening Day roster prior to Wednesday's announcement.

Mateo has spent eight seasons in the Minors between the Yankees and A's systems, batting .267/.325/.422 with 52 homers and 283 steals. He's currently 13th on the Padres' top prospects list, per MLB Pipeline, and was expected to split time at shortstop, second base and the outfield.

Lat tightness for Castillo
The Padres entered camp with one of the deepest bullpens in baseball -- a useful commodity in a short season with extra importance on every regular-season game. That depth is already being tested.

Left-hander José Castillo exited Tuesday night's intrasquad game with lat tightness, Tingler said. The team's early diagnosis is a lat strain, but Castillo will undergo further tests, and no timetable has been given for his return.

The injury is particularly concerning considering Castillo's history. He missed the first four months of the 2019 season with an elbow injury. Castillo pitched two-thirds of an inning upon his return, then sustained an injury to a ligament connecting to his left middle finger, which sidelined him for the remainder of the season.

"He dealt with a couple different issues, including the finger," Tingler said. "The lat strain -- we don't think, initial reaction, that they're related."

Castillo figured to be a key weapon among the team's late-inning options. He posted a 3.29 ERA with 52 strikeouts over 38 1/3 innings during his rookie season in 2018. Fellow lefties Drew Pomeranz and Matt Strahm would likely be called upon to make up for Castillo's absence.

Rotation picture crystallizes
Six days into Summer Camp, the Padres' primary rotation options have all made one appearance in the team's nightly intrasquad games.

Tingler has fixated on 12 as the number of starting pitchers he'd like to have available for the season, with additional depth needed because of concerns about the coronavirus.

That means prospects Adrian Morejon and Michel Baez will be built toward a starter's workload during camp, and they will pitch Wednesday night. Both have been used in a number of different roles in the past, and nothing is off the table for them in 2020.

"The plan is to build them up, and they're in the competition for all those options, whether it's starting or long relief," Tingler said.

As things stand, it seems likely Chris Paddack, Dinelson Lamet, Garrett Richards and Zach Davies are in the rotation. There's still competition for the last spot, with Joey Lucchesi as the favorite.