A drug delivery device (100) for administering a low dose of a medicament includes a housing (111) and a drug reservoir (101) disposed in the housing (111). A needle (135) is connected to the drug reservoir (101). A pressure applying member (113) is movably connected to the housing (111) and is movable between first and second positions. The pressure applying member (113) does not apply pressure to the drug reservoir (101) in the first position and applies pressure to the drug reservoir (101) in the second position to dispense medicament stored in the drug reservoir (101). A method of administering a low dose of insulin to simulate a first-phase insulin response of a pancreas is also disclosed.