None of those who came in contact with Duncan before he was put in isolation have shown signs of contracting the virus.
"[I'm] looking forward to shaking some hands of 48 people who need to get back into society," Dallas County Judge Clay Jenkins told NBC Dallas-Fort Worth.
Amid the relief, more than 70 health workers who cared for Duncan when he was in isolation remain under watch.
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Two nurses at the hospital, Nina Pham and Amber Vinson, contracted the deadly virus and have been hospitalized. "They are blameless in this situation," Jenkins added. "They are victims of Ebola. They are not at fault for contracting this disease in any way."
Troh's daughter, Youngor Jallah, who also ended her monitoring period Monday, has stayed in an apartment she shares with her partner and their children, according to The Associated Press.
"I'm telling you, just to step outside will be so great," she told the AP. "To hug my mom and grieve for Eric, not over the phone like we've been doing, but in the flesh."
More good news came from the World Health Organization with its declaration that Nigeria was free of Ebola cases. A Liberian-American man carried the virus to Africa's most populous country in July, and 19 people became infected.
Ebola has killed 4,546 people across Liberia, Guinea and Sierra Leone, the three worst-affected countries. Nigeria had 20 cases in total, of which eight died.
More than 9,000 people in West Africa have been infected with Ebola, and half have died, sparking fears in the U.S. and elsewhere that the virus could spread.
Ebola spreads by close physical contact with the bodily fluids of someone who is infected and symptomatic. But despite the threat of the Ebola crisis growing exponentially in West Africa, Americans have little reason to fear the disease spreading here, experts told NBC's "Meet the Press" on Sunday.
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The Pentagon is fielding a 30-person expeditionary medical support team to provide immediate assistance to civilian health professionals in the U.S. if additional Ebola cases arise. The team will include 20 critical care nurses, five doctors trained in infectious disease and five trainers in infectious disease protocols, the Pentagon said in a statement.
New York Senator Charles E. Schumer on Sunday called on the Center for Disease Control to station a team of experts in New York City, saying JFK and Newark airports receive the majority of traffic coming from West Africa.
—The Associated Press contributed to this report.