NEW YORK — The nation is heading toward the worst outbreak of West Nile disease in the 13 years the virus has been on this continent, federal authorities said Wednesday.

But it is unclear where and how far cases will spread. Dallas declared an emergency last week; West Nile deaths have been concentrated in Texas and a few nearby states, including Louisiana, Mississippi, Oklahoma, and South Dakota.

So far this year, there have been 1,118 cases and 41 deaths reported to the Centers for Disease Control and Prevention.

‘‘That’s the highest number of cases ever reported to the CDC by the third week of August,’’ said Dr. Lyle R. Petersen, head of the agency’s division of vector-borne diseases. ‘‘And cases are trending upward.’’

About one case in 150 is serious enough for the patient to be hospitalized. But 10 percent of the hospitalized die; others may be left paralyzed.