Radio Free Europe, which has journalists in the country, reported that Turkmenistan has tried to squelch even private conversations about the virus. Plainclothes police officers detain those who gossip about it in food lines, the news organization said. Despite sharing a border with Iran, which has reported more than 44,000 infections, Turkmenistan’s government says the country has not had a single case.

“To me it’s very short sighted,” Dmitri Trenin, the director of the Moscow Carnegie Center, said of the former Soviet leaders’ minimizing the epidemic. “If you say, ‘Well, we are an island in a stormy sea and that is because of me,’ then you’ve cloaked yourself in armor that doesn’t allow a single chink. If there is one chink, your credibility goes down.”

And they are not likely to be able to hold out long, he added. “Look around — they are surrounded by countries with multiple cases.”

The president of Tajikistan, Emomali Rohman, who has been in power since soon after the Soviet collapse in 1991, initially embraced precautionary measures like closing mosques but then reversed course, without public explanation.

The message, though, was clear: He would defy the virus. As with the region’s other long-serving potentates, stability has been a cornerstone of Mr. Rohman’s political image. He casts himself as a fatherly figure who brought normalcy after the mayhem of the Soviet breakup and an ensuing civil war.

His playbook for holding together a wobbly state has been to deny vulnerability, first to terrorist attacks, which have been misrepresented as opposition violence, and now to the pandemic. As late as March 22, long after most nations had begun strict social distancing, Mr. Rohman gathered about 12,000 students in a stadium for a celebration of the Persian new year, Nowruz.