At best, half of Central Virginians who need public mental health care might not get it, according to a study by a University of Virginia economics professor. At worst, nearly nine in 10 might not get care. UVa’s Steven Stern estimates that 9,634 to 38,022 people in the region annually fall beyond the reach of the Region Ten Community Services Board, which served an average of 4,813 people a year from 2008 to 2010.