。
Mother has been sick since last Thursday.
Literal
Mother [topic-は] this before [gen-の] Thursday [from-から] continuously sick is.
Japanese uses the plain present です for a state that started in the past and continues — English forces a perfect continuous ('has been'). The adverb ずっと reinforces the 'the whole time since then' reading, and から marks the starting point. この前の木曜日 literally 'this-before's Thursday' is the idiomatic way to say 'last Thursday' (the Thursday just past, not a generic previous one).