Zeezrom's belief allows for him to be healed. We have an interesting juxtaposition of concepts that we consider to be different. We have a physical ailment, and a spiritual sickness. When Alma "heals" the one, he also heals the other. What have the physical and the spiritual to do with each other?
While they may not be causally linked, the faith required for the healing of the body is apparently also simultaneously sufficient for the healing of the soul. We find in Matthew the following event:
Matt. 9:2-7
2 And, behold, they brought to him a man sick of the palsy, lying on a bed: and Jesus seeing their faith said unto the sick of the palsy; Son, be of good cheer; thy sins be forgiven thee.
3 And, behold, certain of the scribes said within themselves, This man blasphemeth.
4 And Jesus knowing their thoughts said, Wherefore think ye evil in your hearts?
5 For whether is easier, to say, Thy sins be forgiven thee; or to say, Arise, and walk?
6 But that ye may know that the Son of man hath power on earth to forgive sins, (then saith he to the sick of the palsy,) Arise, take up thy bed, and go unto thine house.
7 And he arose, and departed to his house.
Jesus performs a healing that is similar in some ways to the healing of Zeezrom by Alma. There are physical symptoms, and those physical symptoms are cured. However, there is also a forgiveness of sins, both for the man lying on a bed in the land of Israel, and for Zeezrom lying on a bed in the land of Sidom.