。
She has been ill since last week.
Literal
She [topic-は] last-week [since-から] sick is.
である is the formal/literary copula — functionally equivalent to だ or です but used in written, academic, or official contexts. Where 病気だ is casual and 病気です is polite, 病気である is formal and declarative. This copula appears frequently in newspapers, legal texts, academic writing, and formal speeches.