Who might be immuno-compromised or have a weakened immune system? – Examples of persons with weakened immune systems include those with AIDS; cancer and transplant patients who are taking certain immunosuppressive drugs; and those with inherited diseases that affect the immune system. The risk of developing severe disease may differ depending on each person's degree of immune suppression.Who might be immuno-compromised or have a weakened immune system? – Examples of persons with weakened immune systems include those with AIDS; cancer and transplant patients who are taking certain immunosuppressive drugs; and those with inherited diseases that affect the immune system. The risk of developing severe disease may differ depending on each person's degree of immune suppression