The news that a nurse who’d treated Thomas Eric Duncan has Ebola herself puts the lie to the Centers for Disease Control and Prevention’s repeated assurances for months that “US hospitals can safely manage patients with Ebola.”

The nurse is now in isolation at the same Dallas hospital, Texas Health Presbyterian.

Dr. Dan Varga, the chief medical officer, confirmed that she became infected despite wearing CDC-prescribed protective gear, including waterproof gown, gloves, goggles and a plastic face shield while caring for Duncan, who’d contracted Ebola in Liberia.

Eighteen other hospital staff are being watched for symptoms.

No wonder. Treating Ebola patients is a deadly job. More than 233 doctors and nurses have died from Ebola in Africa this year.

Many had limited equipment and training, but the fatalities also include renowned epidemiologist John Taban Dada, medical director of Liberia’s two largest hospitals, as well as UN doctors and two health-care workers from the highly trained Doctors Without Borders teams.

There is no room for error, explains Anja Wolz, a Doctors Without Borders nurse. To put on and take off protective gear, “we use a buddy system — we’re responsible for ourselves but must also put our lives in the hands of colleagues: One mistake can lead to infection.”

That is what happened to a Spanish nurse’s aide, Maria Teresa Romero Ramos. She wore a protective “space suit” on the two occasions she came close to an Ebola patient in a Madrid hospital, but she inadvertently touched her cheek with her gloved hand while removing the suit.

Now she has Ebola and is clinging to life.

Peter Piot, who discovered the Ebola virus in 1976, isn’t surprised that even in modern, equipped hospitals, caregivers get infected. “The smallest mistake can be fatal.”

Explaining the Texas nurse’s infection, CDC chief Dr. Tom Frieden said, “At some point there was a breach of protocol, and that breach in protocol resulted in this infection.” That’s right: He blamed the nurse.

Frieden predicts more health-care workers will get Ebola if they too made mistakes. But doctors and nurses shouldn’t face an ultimatum: Make a mistake, and you die.

US hospitals are ridden with mistakes. Common infections like C. diff and Staph rage through hospitals because doctors and nurses sometimes forget even the most basic protocol: washing hands.

I’ve been an advocate for patient safety for over a decade, and I know that hospitals unable to stop these infections can’t stop Ebola. To claim they can is a lie.

Many hospitals also lack equipment. Texas Health Presbyterian nurses relied on face masks, which is what the CDC prescribes. But other experts say they should have respirators.

Epidemiologists at the University of Illinois explain that Ebola “has the potential to be transmitted through aerosol particles both near and at a distance from infected patients, which means that health-care workers should be wearing respirators, not face masks.”

Indeed, CDC and Emory University staff wore respirators when they cared for two Ebola-infected health-care workers evacuated from Africa. It’s easy to see why some health-care professionals complain of a double standard in the CDC’s protocols.

Not that respirators guarantee safety. Even with them, says Johns Hopkins nurse Trish Perl, “the physical exhaustion and emotional fatigue that come with caring for patients infected with Ebola increase the chance of an inadvertent exposure to bodily fluids” when removing gear.

National Nurses United, a labor union, is protesting the lack of equipment and training. Eighty-five percent of nurses surveyed by NNU said they hadn’t received Ebola training.

Then there’s the lack of staff. It takes 20 full-time medical staff to care for one Ebola patient. Texas Health Presbyterian cordoned off its ICU for Ebola, and is diverting emergency patients to other hospitals. Not all communities have several hospitals.

So Frieden is simply wrong to claim hospitals are ready. What of his insistence that Ebola won’t spread “widely” here? At best, that’s a weasel word: Even one nurse facing death is too many.

Betsy McCaughey is chairman of Reduce Infection Deaths and a senior fellow at the London Center for Policy Research.