The Ebola virus can be transmitted to other people only through bodily fluids when an infected individual begins to show symptoms. At the onset of illness, the amount of virus in the body is generally low, so the risk of infection is also considered small.

As the disease progresses, the amount of virus in the body multiplies and so does the risk of contagion.

Dr. Spencer’s fiancée, Morgan Dixon, has been quarantined at Bellevue Hospital Center. Officials said she would be allowed to return to the apartment she shared with Dr. Spencer, which has been cleaned, and carry out the rest of her quarantine there.

Two other friends whom he had contact with have also been quarantined. None of them have shown any symptoms of illness.

Health officials said there was no risk to patrons at any of the businesses Dr. Spencer visited, though one of them, a bowling alley in Williamsburg called the Gutter, said on its Twitter feed Friday night that it was still waiting for a cleaning crew to arrive and had not yet reopened.

The officials decided that subway cars did not need to be taken out of service and disinfected, since Dr. Spencer rode the trains before he developed a fever and, in any case, the virus can survive only a few hours on a surface.

“There is the pure science and the protocols that must be put in place based on that science, in terms of what we know and what can come from that,” said Dr. Irwin Redlener, the director of the National Center for Disaster Preparedness at Columbia University and a special adviser to Mayor de Blasio. “On the other end of the spectrum, there is the world of abundance of caution. Public officials are constantly trying to find the right balance.”