The CDC's Director Dr. Tom Frieden briefed President Obama about the latest Ebola infection in Texas by phone on Tuesday.

On Wednesday he joined "CBS This Morning" to discuss the possibility that the infected person transferred the disease to others.

"The bottom line is we're stopping this in its tracks in the U.S.," Frieden said. "And I'm confident we can do that because of our strong health care and infection control, and our strong public health system."

Frieden said the process is called contact tracing. The CDC will determine who could have been in contact with the infected person and then monitor those people for 21 days. (The victim's name and age have so far not been revealed.)

If those under watch develop a fever or other symptoms, they're put in isolation, Frieden said.

"By doing that, we stop the chain of transmission from continuing," Frieden explained. "That's the tried and true public health measure that will contain this case from spreading widely."

One of the most important points that Frieden stressed was that the man was not infectious when he boarded the plane. Furthermore, anyone leaving from Liberia with a fever is not permitted to fly.

"He didn't develop his first symptom until at least four days after he arrived in this country," Frieden assured. "The incubation period from exposure to infection can be as much as 21 days, so for those 4 days and the days he was on the plane, he could not have infected anyone."

The problem though, is that he did have symptoms at least four days before he was isolated.

The CDC is now determining how many people he came in contact with during that period. Anyone they find, Frieden said, will be monitored for symptoms.

"We'll go through every minute of each day with his family to understand who might have been exposed and every healthcare interaction he had to see if there are health workers who might have been exposed," Frieden said.

Frieden wants to assure Americans that the CDC knows how to stop Ebola - and they will.

While it's possible one or two people may develop symptoms after this case, Friedman said, the bigger picture is still their biggest concern.

"We have surged to respond to that epidemic, but stopping it at the source is the single most effective way to protect Americans," Frieden said.