Sickness radical 疒 - a person leaning on a sickbed under a roof. The indexing radical, anchoring 痘 in the disease family with 病 (illness), 痛 (pain), 疫 (epidemic), 疹 (rash). Almost every name for a specific ailment in Chinese sits under this wrapper.
Inner 豆 supplies the sound directly - dòu matches the whole reading - and adds a vivid semantic image: the round pustules of smallpox look exactly like scattered beans on the skin. Originally meant 'ritual vessel on a stand'; later reused for 'bean'. Same phonetic in 逗 (tease), 蚪 (tadpole).
