Monkeypox, once a relatively obscure virus endemic to Africa, has bloomed into a global threat, infecting more than 20,000 people in 75 countries and forcing the World Health Organization to declare a worldwide health emergency.

On Thursday, New York State and San Francisco declared emergencies of their own. But even as the national tally nears 5,000 cases and experts warn that containment is slipping away, federal health officials have not followed suit.

One reason: This virus — unlike the coronavirus — is a known enemy, officials say. Doctors understand how it spreads, and there already are tests, vaccines and treatments.

But to scientists, the accumulating research presents a more complicated, and challenging, picture. The virus remains a mystery in some important ways, not exactly behaving in ways that researchers saw during sporadic outbreaks in African countries.

Scientists are racing to answer three questions in particular that will determine how quickly monkeypox can be stopped — if it can be stopped at all.

Exactly how is the virus spreading?

At the beginning of the outbreak, health officials asserted that the virus spread through respiratory droplets emitted when an infected person coughed or sneezed, and through close contact with pus-filled skin lesions or bedding and other contaminated materials.

All of that was true. But it may not be the whole picture.

More than 99 percent of the people infected so far are men who acquired the virus through intimate contact with other men, according to the Centers for Disease Control and Prevention. Only 13 women and two young children had been diagnosed with monkeypox as of July 25.

Researchers have found the virus in saliva, urine, feces and semen. It is unclear whether those fluids can be infectious and, in particular, whether the virus can be transmitted during sex by means other than close skin-to-skin contact. But the pattern of spread so far, along sexual networks, has left researchers wondering.

It is clear, however, that monkeypox does not spread easily and has not yet spilled into the rest of the population. The average person is not at risk from store-bought clothes, for example, or from a fleeting interaction with an infected person, as some social media posts have suggested.

According to the C.D.C., people without symptoms cannot spread monkeypox. But at least one study has detected the virus in men who did not experience any symptoms. The pattern of symptoms has also diverged from that observed in previous outbreaks.

In Africa, some people became ill after touching infected animals, consuming bushmeat or using medicinal products made from the animals. They often developed fever and body aches, followed by a characteristic rash first on the face, palms and feet, and then over the whole body. Infants and pregnant women seemed at highest risk of severe symptoms.

In the outbreak outside Africa, many patients don’t have fever or respiratory symptoms at all, and the rash is often limited to a few lesions in the genital or rectal area, which can easily be mistaken for various sexually transmitted infections.

Britain has now modified its official description of monkeypox to include lesions in the mouth, and anal or rectal pain and bleeding. Some scientists have speculated that the presentation of the disease in Western countries may accurately reflect the virus’s natural course.

Is one dose of the vaccine sufficient?

Jynneos, the safer of two vaccines for monkeypox, is made by Bavarian Nordic, a small company in Denmark. Supplies have been severely constrained, and the Biden administration moved slowly to acquire additional doses as the virus spread.

Now, federal officials have ordered nearly seven million doses, which will arrive in batches over the next months. So far, the administration has shipped about 320,000 doses to states. The Food and Drug Administration said on Wednesday that it had approved another 800,000 doses, but it was unclear when they would be distributed.

Jynneos is supposed to be administered in two doses 28 days apart. But some cities, including Washington and New York City, are holding back second doses until more become available, emulating a strategy adopted by Britain and Canada.

Federal health officials have advised against deferring second doses. But in studies, a single shot of Jynneos appears to be protective for up to two years. If that finding holds true in the real world, then postponing additional shots may help officials contain the outbreak by immunizing more Americans.

Britain held back second doses of the Covid vaccine early in the pandemic, when supplies were low, noted Tinglong Dai, an expert in vaccine supply at Johns Hopkins University. “The benefit of prioritizing first doses outweighs the risk,” he said.

There may not be much choice as eligibility widens and more at-risk people seek shots. Some jurisdictions already have expanded the groups eligible for immunization to include sex workers, patients of sexual health clinics, and clinicians and other employees who may be exposed to the virus at work.

In Rhode Island, Emily Rogers, a 29-year-old medical anthropologist, said she was able to call the local health department and get an appointment “very, very quickly.”

Ms. Rogers qualified for the shot because she sometimes has sex with men at high risk for monkeypox infection. Nobody questioned her eligibility. “They weren’t weird about that at all — it was a very smooth process,” she said.

Because of the shortage, the vaccine is being offered only as a preventive measure, even though it can mitigate symptoms if given within days after exposure.

David Baldwin, 45, a music professor in New York, qualified for vaccination only because doctors didn’t believe he was already infected. (His initial symptom was rectal pain.) “As a result, I think, I never developed lesions on my body,” he said.

How well does drug treatment work?

In 2018, the F.D.A. approved a drug to treat smallpox called tecovirimat, or TPOXX, based on data from animal studies. There are only limited data on its use in people.

Supply is not an issue: The national stockpile holds about 1.7 million doses. Yet the drug has been difficult to acquire, and that has meant that ambiguities about how well and for whom the drug works have persisted even as case counts rise.

Because tecovirimat is not approved specifically to treat monkeypox, it can only be prescribed through a cumbersome “investigational drug protocol” that, until recently, required doctors to send the C.D.C. detailed reports, a journal maintained by the patients to record their progress and photographs of the lesions.

With so many hurdles, many clinics did not offer tecovirimat at all; even physicians at well-funded institutions were managing to treat only two or three patients per day.

Nephi Niven Stogner, 39, sought help for monkeypox symptoms on July 8. He was in excruciating pain and tried to get tecovirimat, but was told that others were sicker and needed it more.

While he waited for the drug in isolation, three new lesions popped up on his back. “It’s like your sentence is getting extended,” he said.

Mr. Stogner finally got his first dose on July 21. Within 24 hours, his “lesions went from swollen and red to flat, dark spots,” he said.

Such delays led the C.D.C. to ease the rules for access to tecovirimat. The agency now requires fewer patient visits, samples and forms, and allows doctors to assess patients virtually.

Wider use should mean that scientists and health officials will gain a better understanding of the drug’s efficacy. The new requirements will help the C.D.C. “determine if and how well this drug works for monkeypox patients,” noted Kristen Nordlund, a spokeswoman for the agency.

The National Institute of Allergy and Infectious Diseases is planning a clinical trial of tecovirimat in adults with monkeypox infection, including people living with H.I.V., which may begin this fall. The agency is collaborating with Siga Technologies, which manufactures the drug, on another trial in the Democratic Republic of Congo, where the virus is a longtime scourge, also expected to begin this fall.