'Contagious' traces to Latin 'tangere' (to touch) — kin to 'tangent,' 'tact,' and 'intact.'
Capable of being transmitted from one person to another through direct or indirect contact; tending to spread rapidly.
From Late Latin contagiōsus (communicable by contact), derived from Latin contagiō (a touching, contagion), from contingere (to touch closely), composed of con- (together) + tangere (to touch). The PIE root *teh₂g- (to touch, to handle) underlies the entire tangere family. The adjective suffix -ōsus (English -ous) means full of or characterised by, so contagiōsus literally means characterised by contact. The concept entered English from Old French
The Latin 'tangere' (to touch) is behind an enormous English family: 'contact' (touching together), 'tangent' (touching a curve), 'tangible' (touchable), 'intact' (untouched), 'tact' (a sensitive touch in social situations), and 'contagious' (spreading through touch). Touch is one of the most metaphorically productive concepts in Western vocabulary.