Low death rate from infectious diseases in modern hospitals are attributable to modern hospitals having isolation facilities, where infectious patients are quarantined, and having better technological equipments used to diagnose and treat infections in its early stages.
Hospitals now have areas that cater to different types of medical conditions. Areas like the intensive care units, labor and birthing rooms, isolated rooms, etc. Unlike hospitals in the early ages where everyone is placed in wards regardless of the extent of their sickness.
Vaccinations are also readily available for everyone which lessens the chances of acquiring infectious diseases and spreading them to unsuspecting people.