expression, suru verb (special)
feign illness; pretend to be ill
Rare, literary expression for pretending to be sick. Modern Japanese more commonly uses 仮病を使う or 病気のふりをする.
彼は病と称して仕事を休んだ。
He feigned illness and took a day off work.
Common noun for feigned illness; used in 仮病を使う (to feign illness). 病と称する is a rarer, more literary verb phrase.
Compound of 病 (illness) + と (quotative particle) + 称する (to call, to claim). The exact historical derivation is uncertain, but it follows a classical pattern of claiming a state.