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DALLAS (CBSDFW.COM) – The top administrator for Dallas County said Saturday it’s a “critical weekend” in the Ebola containment effort as the first people who had contact with Thomas Eric Duncan after he became ill begin emerging from a 21-day monitoring period.

Ebola’s maximum incubation time frame is 21 days, meaning the people exposed to Duncan after his arrival in Texas from Liberia in late September are now reaching the point where they don’t have to worry about catching the virus. His family and friends who were near him can come out of quarantine after Sunday, at midnight. The Centers for Disease Control and Prevention said Saturday that 14 people have completed the “active surveillance” period.

Health officials have broken down Duncan’s contacts in two main groups: The 48 people who had contact with him before his hospitalization and about 70 medical workers who were involved in his care. Many of the 48 people will be out of the 21-day period after Sunday, also at midnight.

The estimated 70 workers were asked this week to sign a legal form agreeing not to travel on airplanes, to consult with public health officials before taking mass transit and to avoid public places. Judge Clay Jenkins, the county administrator, said Saturday that all but about 10 people had signed the agreement and that everyone was adhering to the pledge.

He estimated that about 25 of the isolated health care workers are staying at the hospital, an offer made by the employer for people who didn’t want to risk staying at home with their families.

Jenkins said the county is still bolstering plans in the event more people get sick. That includes forming a “go team” of about 50 medical specialists from Parkland Memorial Hospital, the county hospital, to respond if there’s another case.

Meanwhile, pastors are returning to the pulpit Sunday with Ebola on the mind of many parishioners. Dallas Mayor Mike Rawlings said Saturday he held a conference call with 80 pastors a day earlier, during which they discussed the need to welcome anyone who had been cleared from the monitoring lists. He said he had similar calls with business and apartment building owners.

“We need you to ask your congregation to confront their fear with facts,” he told the religious leaders during the call, later adding, “You know the stories, and you know the verses, and you know the words that can heal and also uplift.”

Ebola scares continue to crop up in Dallas and elsewhere. On Saturday, a woman fell ill at a train station and said she once stayed at the same apartment complex where the 41-year-old Duncan lived. It was later determined that she had no contact with Duncan and was not at risk of having Ebola.

Jenkins said officials are getting several calls an hour from people who think they have Ebola or might have been exposed to the virus.

“Actually, the operation is absorbing those pretty well and going through those pretty quickly,” he said.

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