There are many ways to address your task. Because this image was originally B&W, your job will be easier, because essentially you need only adjust the luminosity of the stained areas. Usually this can be accomplished with a combination of curves (on selected areas), and Dodge/Burn.
However for this image, because the stains are all red, I would add a B&W adjustment layer in Photoshop, and drag the Red slider to the right. This takes about 5 seconds and gives you a good starting point from which you can use the clone stamp / healing brush or a D&B layer or combination to refine your work. The sample attached shows only the addition of the B&W adj layer with the Red slider adj.