染 means 'to dye' or 'to be tainted by' — the same verb you use for
染发 'dye one's hair' or
染色 'to color'. Picture illness 'staining' a person, the way dye soaks into cloth. Distinguish from
生病 (shēngbìng) 'to get sick' which is more general;
染病 specifically implies infection from an outside source.
