A disease which spreads by contact

One word substitute is Contagious.

Infectious: (of a disease or disease-causing organism) liable to be transmitted to people, organisms, etc. through the environment.
Contagious: (of a disease) spread from one person or organism to another, typically by direct contact.
Contiguous: sharing a common border; touching.
Contextual: depending on or relating to the circumstances that form the setting for an event, statement, or idea.