。
She's been sick in bed since last Monday.
Literal
She [topic-は] this-time-before [genitive-の] Monday [from-から] sickness [due-to-で] is-sleeping.
病気で寝ている is a stock collocation for 'be sick in bed' — 病気 ('illness') + the causal で + 寝ている ('is lying down / sleeping'). The で here is causal: '(she's lying down) because of illness.' 寝る covers both 'sleep' and 'lie down' in Japanese; the resultant-state ている locks in the ongoing state. Combined with から marking the starting point, the sentence gives a complete picture of an illness that's persisted from a known date. Note that calling out from work or school for illness in Japan typically involves direct contact with the workplace/school — the institution expects to know.