My mother has been sick in bed since the end of last month.
Literal
Mother [topic-は] last-month [possessive-の] end [from-から] continuously sick [because-of-で] is-sleeping
先月の終わりからずっと = 'continuously since the end of last month.' から marks the starting point, ずっと = 'continuously/the whole time.' 病気で寝ている = 'bedridden due to illness.'