'disease-spreading' is a compound formed from 'disease' and 'spreading'. 'disease' originates from Old French 'desaise' (from 'des-' "lack, absence" + 'aise' "ease"), and 'spreading' comes from English verb 'spread' (Old English 'spreadan').

'disease' developed via Middle English 'disese'/'diseas' from Old French 'desaise' and eventually became modern English 'disease'. 'spread' comes from Old English 'spreadan', later Middle English 'sprede', giving modern English 'spread' and the present participle 'spreading'.

Initially, 'disease' literally suggested a 'lack of ease' and came to mean 'illness'; 'spread' originally meant 'to stretch out or extend' and came to mean 'to distribute or propagate', so the compound came to mean 'causing illness to propagate'.