We consider the differential microwave imaging for continuous monitoring of hemorrhagic brain strokes where our aim is to determine the change of bleeding in sequential time frames. The scattered electromagnetic field is measured in two different time steps, and the difference in the scattered field is used as the data of the inversion scheme. The imaging is performed via contrast source inversion. However, since the data of the inversion scheme consists of the difference of the scattered field measurements, the algorithm produces a differential contrast function instead of a complete reconstruction. This function carries information about the difference in the electromagnetic parameters of the brain, that is the relative size of the blood region, between two measurements. The numerical simulations with a realistic head model demonstrate that the method is capable of detecting changes in multiple blood regions, and provides information about the locations and the types of these changes.