Not only are the Oakland A’s mired in one of its worst starts to a season in franchise history, but also players are dropping like flies.

Closer Trevor Rosenthal, who has spent the entire season on the injured list with shoulder inflammation, flew to Dallas on Monday to meet with Dr. Gregory Pearl. Manager Bob Melvin said the meeting has been in the works since Rosenthal struggled to bounce back from his outings during spring training, which were few and far between.

Having not held a lead yet, the A’s haven’t needed to tap in a closer. But this is not a promising start, health-wise, for the second-highest-paid Athletic for the 2021 season. Rosenthal has been on medication for his shoulder fatigue since he landed on the IL.

Matt Olson will miss Tuesday’s game after suffering a left knee contusion crashing into a wall on Monday. Olson had an MRI that revealed no structural damage. He is day-to-day, but this is the first game the A’s iron man has missed since a hamate bone fracture took him out of the first 35 games of the 2019 season. He played in all 60 of the games in 2020.

A day after losing utility player Chad Pinder to a left knee sprain, the A’s placed relievers Burch Smith and Reymin Guduan on the 10-day injured list.

Right-handed reliever Smith will sit out with a groin strain and left-handed reliever Guduan with a left thumb sprain incurred in a collision with the Los Angeles Dodgers’ Cody Bellinger in a race to first base in the ninth inning of Monday’s 10-3 loss. Smith allowed a run with a strikeout in three innings this season, but “it’s going to be a little bit” until his return, Melvin said.

The A’s called up outfielder and first baseman Seth Brown and right-handed reliever Jordan Weems to fill the roster spots. Brown, 28, made his debut with the A’s in August 2019 and collected 22 hits in 28 games which included eight doubles and two triples. But his big league time since has been limited. He played seven games without a hit in 2020. The left-handed hitter had a solid spring this year, particularly later in the Cactus League schedule, going 7 for 31 with three home runs.

Guduan joined the A’s bullpen in the wake of closer Rosenthal’s shoulder injury to start the season. The 29-year-old has had a rough go of it, used in mop-up innings with the A’s on the wrong end of several blowouts already. He’s given up nine earned runs in 2 2/3 over three appearances.

Guduan and Smith join a long list of A’s regulars now sitting on the injured list: Pinder, Rosenthal and starter Mike Fiers are on the 10-day IL. Outfielder Ramón Laureano returned to the lineup for Tuesday’s game against Clayton Kershaw after missing three games with a wrist injury he suffered sliding into first base in the second game of the season. Sean Murphy returned Monday from his own wrist injury that he suffered when hit by a pitch on Opening Night.

Pinder was shortstop Elvis Andrus’ backup shortstop. The A’s anticipate having Andrus play shortstop until Pinder’s return. In an emergency, Matt Chapman can slide over to shortstop and Jed Lowrie can play third base.

The A’s injuries only add to their difficult start to the season. The team went 0-5 for the third time in franchise history and the first time since 1987. They’ve been outscored 45-12 through their first five games against the Dodgers and Astros.

The bullpen has been the most-used in MLB so far. A’s relievers have pitched 23 innings and hold a 7.43 ERA, sixth-worst in the league through five games.