The Hungarian government is trying to tame the wave of medical doctors leaving the country by offering them money to stay. But as the application deadline approaches later Monday, few have expressed interest in the government scheme.

Under the program, Hungarian doctors can receive 100,000 forints ($530) net on top of their monthly salaries for a period of five years. This means the doubling of their wages during that time. In return, the program's participants have to make a commitment to practice medicine in Hungary for...