(CNN) President Donald Trump , despite claiming otherwise, has fixated on the television ratings of his daily coronavirus briefings, comparing the numbers to television shows such as ABC's "The Bachelor." And like the dating competition he's cited five times on Twitter to boast about his viewership, the casting of his program is key.

Until Wednesday, the roster this week hadn't included Dr. Anthony Fauci , the nation's top infectious disease expert, who last week described participating in Trump's daily marathon coronavirus briefings as "really draining." He went for a four-day stretch without appearing at the White House podium -- a change from earlier days in the outbreak, when he was a more regular fixture.

It has included officials such as Lt. Gen. Todd Semonite, the head of the Army Corps of Engineers; Brett Giroir, the administration's testing czar; and Treasury Secretary Steven Mnuchin, who is overseeing efforts to salvage a badly weakened economy.

Aides have said there is little to read into the shifting personnel accompanying Trump to his briefings, indicating the day's assemblage has more to do with the particular message being sent and not each official's current standing. At other times, Trump has picked at random who will join him in the briefing, with some aides only finding out moments before it starts.

Still, for a President who now views the daily briefings as essential to his political future and insists on holding them even on weekends, the makeup of the cast has been a regular preoccupation.

Trump has told aides that he -- and not his underlings -- generate the biggest numbers, even more than the doctors or other professionals on the task force he assembled to combat the public health crisis.

And though he's boasted in private about making stars of his team, Trump has also bristled at suggestions he leave the medical advice and public health recommendations to doctors -- and in particular Fauci, whose candid management of the coronavirus crisis has earned him praise from many but scorn from certain Trump allies.

Administration officials, Fauci and even Trump himself have been quick to downplay his previous absences, suggesting he's a busy man combating a once-in-a-generation health crisis. Even on days when he does not appear during the early-evening news conferences, Fauci still attends coronavirus task force meetings in the White House Situation Room, which are led by Vice President Mike Pence.

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On Monday, he departed the White House just after 4 p.m. ET, about 90 minutes before the daily briefing commenced. On Tuesday, he had returned to the National Institutes of Health by late afternoon as Trump and his aides were preparing for the news conference, the start of which focused on the economic fallout from the virus with Mnuchin.

A source close to the coronavirus task force said Fauci is spending less time at the briefings and more time on vaccine development and other efforts aimed at combatting the pandemic. After initially serving as a fixture at most briefings when the task force was first launched, Fauci now waits on White House officials to call him to the West Wing for the more Trump-focused news conferences.

Fauci is telling people around him that he enjoys the extra time at NIH, seeing it as an opportunity to spend more time on the coronavirus. But the doctor's time at the briefings has noticeably dwindled as he has repeatedly offered stark assessments of the pandemic, at times differing with Trump on vaccines and the usefulness of hydroxychloroquine as a potential treatment.

A Rorschach test

Still, Fauci's non-presence at the briefings has become a Rorschach test of sorts for observers of the administration's response to the coronavirus outbreak. Because of his frank willingness to publicly contradict the President on issues such as testing and treatments, Fauci has become a hero to those who believe Trump is mismanaging the crisis. When he is absent, they cry: "Where's Fauci?"

But those same traits -- along with his public caution on reopening the country too quickly -- have earned him the scorn of some of the President's conservative allies, who have cast him as a showboater unwilling to adopt a consistent message.

Those sentiments made it all the way to Trump's own Twitter feed earlier this month, when he retweeted a message criticizing the doctor and calling for his ouster. "Time to #FireFauci," read the message Trump retweeted on April 12 , the same day Fauci said in an interview on CNN that earlier mitigation efforts could have saved more lives.

Afterward, Trump shrugged off the episode, saying he wasn't signaling any frustration with Fauci, who has led the National Institute of Allergy and Infectious Diseases since 1984. And Fauci characterized his comments as hypothetical and took offense when a reporter asked if Trump had forced him to walk back his previous statements.

"Everything I do is voluntary, please," he said. "Don't even imply that."

But it hardly put to rest the lingering questions about where the two men stand. Trump, who famously dislikes being upstaged, has commented to associates that he's turned Fauci into a television star. And polling has shown more Americans approve of Fauci's handling of the crisis than Trump's: a Quinnipiac University survey released on April 8 showed Fauci's handling earning a 78% approval rating compared to 46% for Trump.

White House officials have continued to insist Trump has confidence in Fauci and Trump has downplayed any tensions. And Fauci has suggested daily appearances -- which involve long stretches standing mute as Trump argues with reporters -- aren't an entirely productive use of his time.

"If I had been able to just make a few comments and then go to work, that would have really been much better," he told The Associated Press in an interview last week . "It isn't the idea of being there and answering questions, which I really think is important for the American public. It's the amount of time."

Trump has tacitly acknowledged his briefings have become substitutes for the political rallies he's forgone because of the outbreak. In private, Trump has itched for a return of rallies or at least some type of event out in the country to break up the monotony of the daily briefings. Pence has visited manufacturing plants, something Trump has told aides he'd also like to do soon.

He said last week that walking into the briefing room -- where reporters are spread apart and only a few technicians are allowed to operate cameras -- isn't the same.

"I'm looking at this room and I see all this -- it loses a lot of flavor," he said. "It loses, to me, a lot of flavor."

Marathon briefings

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Recently, Trump has appeared more aware of the time his officials are spending in the White House Briefing Room. He's asked Cabinet secretaries such as Mnuchin, Attorney General William Barr and Secretary of State Mike Pompeo to deliver remarks and answer questions for a spell before returning to their agencies to continue working.

On Monday, after a presentation from Semonite, Trump offered a choice to the commanding general of the US Army Corps of Engineers.

"So, general, you have a choice: You can stay and watch these wonderful people ask us really nice questions or you can go back to building beds," Trump said.

"Sir, I got a lot of building to do," Semonite responded. "I'm going to leave, if you don't mind."

Seconds later, Semonite was gone.

So far, Trump hasn't offered a similar out for Fauci or Dr. Deborah Birx , the immunologist who is acting as the White House coronavirus response coordinator. That means the doctors are often left standing by as Trump meanders onto tangents or gets into heated arguments with reporters.

Unlike Fauci, Birx has attended nearly every coronavirus briefing -- except for a weekend in March when she said she had a "low-grade" fever and stayed home.

She's also avoided publicly breaking with the President on issues like testing and treatments. Trump sees Birx as a required presence at the briefings, sources say, given her colorful, detailed charts that reveal data about the outbreak throughout the US. She has drawn some criticism in recent days for refusing to second-guess Republican governors who are opening their states well ahead of the federal recommendations.

"Each of the governors can decide for themselves whether they have reached specific guidelines in specific areas," she said.

In the days leading up to key decisions -- such as whether to extend the federal social distancing deadlines or the rollout of guidance on reopening states -- Fauci has participated in lengthy sessions with the President debating the issues.

Unvarnished thoughts

In meetings, Fauci isn't hesitant to offer unvarnished thoughts or analysis even when it seems to contradict the President. He's previously warned the speed of developing a coronavirus vaccine isn't nearly where Trump has suggested it could be and he's cautioned that the possible treatments Trump touts in public haven't yet proved effective.

On Tuesday, Fauci's agency seemed to formalize his concerns about possible treatments. The National Institute of Health issued new guidelines advising doctors against using the drug combination Trump has touted loudest, the anti-malarial drug hydroxychloroquine. The guidelines, published online, are meant to guide doctors, nurses and other medical professionals treating patients with Covid-19 and will be updated in real time as more is learned in fighting the pandemic, the NIH said.

Asked about the NIH guidance on hydroxychloroquine and azithromycin during Tuesday's White House coronavirus task force meeting, Trump said: "We'll take a look at that. I'm always willing to take a look."

Fauci, however, wasn't in attendance. At a White House briefing earlier this month, Trump refused to let the doctor answer a question about hydroxychloroquine.

Frank public disagreements between Trump and a top official are virtually unprecedented in his administration. Earlier in the crisis, Trump grew enraged when an official with the US Centers for Disease Control and Prevention suggested the situation would worsen badly in the United States, believing her assessment overly fatalistic.

Blunt candor hasn't always endeared Fauci to Trump either; the President has complained in private when it seems he's being contradicted by the nation's top infectious disease specialist.

Last week, after Fauci indicated that testing and surveillance capabilities still lagged behind ideal levels, Trump offered a curt response.

"I don't know what he said," he responded when questioned about the remark. "Nobody knows."