Texas Gov. Rick Perry said in a news conference Wednesday that “some school-age children have been identified as having some contact” with the confirmed Ebola patient in Dallas.

“These children have been identified and they are being monitored,” Perry said, adding that the public “should have every confidence” that federal, state and local health workers are making sure the virus is contained and treated.

A day after Dallas County Health and Human Services confirmed it was treating the first patient diagnosed with Ebola virus disease in the U.S., it added that it was closely monitoring another possible patient as well.

According to WFAA-TV, all people who were in contact with this first patient are being monitored but one in particular is being watched more closely, a health official told the news station Wednesday.

“Let me be real frank to the Dallas County residents, the fact that we have one confirmed case, there may be another case that is a close associate with this particular patient,” the health department’s director Zachary Thompson told WFAA. “… So this is real. There should be a concern, but it’s contained to the specific family members and close friends at this moment.”

The health department emphasized in a tweet Wednesday that outside of the one patient in isolation at Texas Health Presbyterian Hospital, there are no other confirmed cases in Dallas.

The Centers for Disease Control in Dallas is helping the health department track down anyone who had close contact with the man confirmed to have Ebola, who is receiving treatment after he was officially admitted to the hospital this week. Each person who needs to be monitored will be watched for 21 days.

If anyone develops fever, we’ll immediately isolate them to stop the chain of transmission,” CDC Director Tom Frieden said in an interview with the Associated Press.

The unidentified Dallas patient has been in isolation since Sunday. Health authorities have not revealed his nationality or age. He was listed in serious condition Wednesday, which is a downgrade from critical condition on Tuesday.

Three members of the ambulance crew that transported the man to the hospital tested negative for the virus, but they are restricted to their homes while their conditions continue observation.

The man was vomiting when the ambulance got to the hospital, Dallas city spokeswoman Sana Syed said. The virus is transmitted through close contact with infected bodily fluids.

The ambulance crew is among 12 to 18 people being monitored after exposure to the man. Some are members of his family, but not all, Syed said.

Ebola symptoms can include fever, muscle pain, vomiting and bleeding, and can appear as long as 21 days after exposure to the virus. The disease is not contagious until symptoms begin, and it takes contact with bodily fluids in order for it to spread.

The man left Liberia on Sept. 19, arrived the next day to visit relatives and started feeling ill four or five days later, Frieden said.

Despite monitoring all people who came in close contact with the unidentified Ebola patient after his symptoms would have become infectious, Thompson told WFAA that the virus is contained at this point.

Watch WFAA-TV’s report about the patient in Dallas:

North Texas has a strong Liberian population, the West African country most affected by the virus outbreak. Stanley Gaye, president of the Liberian Community Association of Dallas-Fort Worth, said they’ve been encouraging people to “to stay away from social gatherings.” The CDC, however, has not advised that people avoid large gatherings in this country.

Frieden, the CDC director, has said that they don’t believe anyone who was on the flight with the man who has Ebola are at risk.

“Ebola doesn’t spread before someone gets sick, and he didn’t get sick until four days after he got off the airplane,” Frieden said.

According to the World Health Organization, more than 6,550 people in West Africa have contracted the virus and more than 3,000 have died from it.

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