Isaiah specifically said that Jesus will be stricken and smitten. The Hebrew words for "stricken" and "smitten" mean "violently, to strike" and "give [wounds]...(give) stripes" respectively, according to Strong's Hebrew Dictionary. The vicious whipping that Jesus received on His back (His "stripes") certainly fulfills this part of the prophecy. Isaiah also said that Jesus will bring peace (peace with God) and healing to us.
Consider that if the salvation parts of Isaiah's prophecy apply to us (and certainly they do) then the healing parts of Isaiah's prophecy apply to us also.
Here's that passage in a more literal translation of the Bible (Young's Literal Translation):
Isaiah 53:4 (YLT): "Surely our sicknesses he hath borne, And our pains--he hath carried them, And we--we have esteemed him plagued, Smitten of God, and afflicted."
Isaiah 53:5 (YLT): "And he is pierced for our transgressions, Bruised for our iniquities, The chastisement of our peace is on him, And by his bruise there is healing to us." ...
Isaiah 53:12 (YLT): "Therefore I give a portion to him among the many, And with the mighty he apportioneth spoil, Because that he exposed to death his soul, And with transgressors he was numbered, And he the sin of many hath borne, And for transgressors he intercedeth."
Isaiah said that "our sicknesses he hath borne [taken away] ... And he the sin of many hath borne [taken away]." Notice that Jesus took away all of our sicknesses, just as He took away all of our sins. We receive healing as a free gift by faith, just as we receive salvation as a free gift by faith.
Consider that if the salvation parts of Isaiah's prophecy apply to us (and certainly they do) then the healing parts of Isaiah's prophecy apply to us also.
Here's that passage in a more literal translation of the Bible (Young's Literal Translation):
Isaiah 53:4 (YLT): "Surely our sicknesses he hath borne, And our pains--he hath carried them, And we--we have esteemed him plagued, Smitten of God, and afflicted."
Isaiah 53:5 (YLT): "And he is pierced for our transgressions, Bruised for our iniquities, The chastisement of our peace is on him, And by his bruise there is healing to us." ...
Isaiah 53:12 (YLT): "Therefore I give a portion to him among the many, And with the mighty he apportioneth spoil, Because that he exposed to death his soul, And with transgressors he was numbered, And he the sin of many hath borne, And for transgressors he intercedeth."
Isaiah said that "our sicknesses he hath borne [taken away] ... And he the sin of many hath borne [taken away]." Notice that Jesus took away all of our sicknesses, just as He took away all of our sins. We receive healing as a free gift by faith, just as we receive salvation as a free gift by faith.