"They are people who need our compassion our respect and our love," Jenkins added. "Treat them the way you would want your own family treated if you were in their place and they were in yours."
Jenkins called the reintegration process a "defining moment" and urged Dallas residents to trust the science behind their recommendations.
"We have to believe in science," Jenkins said. "That's what separates us from other mammals."
Among the people leaving quarantine are Duncan's fiancee, Louise Troh; her 13-year old son, Timothy Wayne; Duncan's nephew, Oliver Smallwood; and a friend of Smallwood's, Jeffrey Cole. Those four individuals lived in the apartment where Duncan stayed before and during the early stages of his illness.
Jenkins expressed particular concern for Troh's 13-year-old son, Wayne, who will be returning to Sam Tasby Middle School on Tuesday.
"I'm extremely concerned about Louise's middle school son," Jenkins said. "To be dropped into a pool of middle schoolers after all that he's been through -- I need your help, parents. I need your help to treat that young man with the kind of love you'd want your own son treated with."
Wayne and four other Dallas Independent School District students will return to the classroom on Tuesday. Three other students who had been in quarantine but attended schools in a neighboring district will be enrolled in Dallas Independent School District schools, the superintendent Mike Miles said.
"They've been through an ordeal," Miles said. "I think the schools will be well-prepared."
Through her Wilshire Baptist Church pastor, George Mason, Troh requested post-quarantine privacy.
"Today is a jubilant day for them," he said. "They are really looking forward to getting out and resuming their lives.
"It would be a tremendous gesture on your part to allow them to re-enter the community on their own terms."
Duncan died Oct. 8, and relatives held a service for him in North Carolina on Saturday -- two days before Troh's 21-day quarantine ended.
For the latter part of the quarantine period, Troh was housed in an undisclosed gated community that had been volunteered by a member of the Catholic community in Dallas, Jenkins disclosed. She will remain in that home for a few additional days until she finds a new residence, said Mark Wingfield, an associate pastor at Wilshire Baptist Church.
Jenkins said early Monday morning that one additional contact will be cleared in the next few hours, and four others are expected to be cleared -- based on their last known contact with Duncan -- "in the next two or three days."
Meanwhile, Dallas Mayor Mike Rawlings said health officials continue to monitor 75 people who came into contact with Duncan or his bodily fluids at Texas Health Presbyterian Hospital in Dallas.
But he said that the release of the first 43 contacts from daily monitoring is a sign that the science of Ebola is sound.
"I am particularly lifted up by today because it's starting to show us the science that we talked about at the very beginning is working," Rawlings said.
There are 25 nurses who are being monitored at the hospital rather than in their homes to eliminate any risk to their children, Rawlings added.
"These are human beings, these are nurses," Rawlings said. "In the city of Dallas, I'd love this week to be hug a nurse week.
"We need to go out there and say thank you for all the work that you do. Let's lift these folks up," he added.
As the quarantine period ended in Dallas, there was more news elsewhere related to the Texas Presbyterian staff: After a hospital lab technician who had contact with Duncan's samples was isolated on a cruise ship last week, school officials in the Oklahoma City suburb of Moore said they would not allow students who had been on the ship to return to school this week.
The lab technician last had contact with Duncan's samples more than 21 days ago and has shown no symptoms of the virus, but Moore School District officials said that they were "erring on the side of caution."