'anti-epidemic' is a compound formed from the prefix 'anti-' (from Greek 'ἀντί' meaning 'against') and 'epidemic' (from Greek 'ἐπιδημία / ἐπιδήμιος', via Latin/Medieval Latin into English), so the literal sense is 'against an epidemic'.

'anti-' entered English as a productive prefix via Latin and Old French from Greek 'ἀντί (anti)'; 'epidemic' comes from Greek 'ἐπιδημίας/ἐπιδήμιος' ('epi-' meaning 'upon' + 'dēmos' meaning 'people') that passed into Late Latin/Medieval Latin and Middle English before forming the modern word 'epidemic'. The compound 'anti-epidemic' is a modern English formation used especially from the 19th–20th centuries in public health contexts.

Individually, 'epidemic' originally meant (literally) 'upon the people' referring to disease affecting a population; 'anti-' meant 'against'. Over time the compound came to be used specifically for actions, policies, or characteristics intended to oppose or prevent epidemics (the modern usage focuses on preventive or counteractive measures).