Nigeria, a nation of 180 million, is in recession and battling challenges nearly everywhere: widespread malnutrition in the north, an area that has been ravaged by the Islamist group Boko Haram; a militant uprising in the south, where a group called the Niger Delta Avengers has sabotaged oil infrastructure; and a struggle for land between farmers and herders in the center.
Mr. Osinbajo, the vice president, is a Christian from the south, and he acts a counterbalance to Mr. Buhari, a Muslim from the north. In recent weeks, Mr. Osinbajo has been working on an economic overhaul aimed at securing a World Bank loan to help the government cope with a deficit caused by the drop in oil revenue.
Mr. Osinbajo’s position as acting president may reflect an effort by the government to avoid a repeat of the instability that consumed the country in 2010, when President Umaru Yar’Adua died after a prolonged illness, leaving a power vacuum and prompting a political crisis.
Mr. Buhari left for Britain on Jan. 19, saying he was going on a “short leave” as “part of my annual vacation.” He said that he would return on Feb. 6. But that date came and went, and although officials said he had taken medical tests and received treatment, they would not provide details, prompting intense speculation and uncertainty.
From London, Mr. Buhari was not much more forthcoming, though on Twitter he revealed that he had received visiting Nigerian lawmakers; offered birthday wishes to a former president, Olusegun Obasanjo, and to Mr. Osinbajo; and met with the Most Rev. Justin Welby, the archbishop of Canterbury.
Mr. Buhari’s office announced on Thursday that he would return home the next day but provided few details about his extended leave of absence. The president underwent “routine medical check-ups” during his vacation, his office said, adding, “The holiday was extended based on doctors’ recommendations for further tests and rest.”
Toyin Falola, a professor at the University of Texas at Austin, and the author of several books about African history, said that Mr. Buhari’s refusal to say more about his health reflected deep-seated cultural norms, including fears that disclosing illness would worsen it.
“You cannot look at it from the point of view of the West, where there is a culture of reporting,” he said in a phone interview. “Africans don’t like to report their health, whether it’s a poor farmer or the president.”
The topic may be particularly taboo because several leaders have died in office, the professor said. The nation’s first prime minister after independence in 1960, Abubakar Tafawa Balewa, was overthrown in a military coup in 1966 and died under murky circumstances.
Two military rulers — Maj. Gen. Johnson T. U. Aguiyi-Ironsi in 1966 and Gen. Murtala Muhammed in 1976 — were killed. Gen. Sani Abacha died of a heart attack in 1998 during his leadership, and Mr. Yar’Adua died in 2010 of kidney and heart ailments.
“When you have less of a grip on the management of a nation, then you have bureaucrats and officers taking use of the opportunity for private gain,” Professor Falola said, adding that the months during which Mr. Yar’Adua had been incapacitated were “a maximum period of greed.”
Mr. Buhari, a former general, was Nigeria’s leader under military rule from 1983 to 1985. Three decades later, he made a political comeback, defeating President Goodluck Jonathan, who had succeeded Mr. Yar’Adua, in a 2015 election that was generally seen as free and fair. It was the first time an incumbent president in Nigeria had been ousted peacefully, via the ballot box.
“I think he should use this opportunity, as much as he can, to improve communication and transparency,” Professor Falola said of Mr. Buhari. “If his doctors have told him that he has a life-threatening illness, and that he cannot survive, he should ensure an effective transition of power. But maybe it’s a manageable disease. We just don’t know.