Houses are not that airtight. Long before a house gets airtight enough to maintain a pressure differential efficiently, the occupants will get ill as off-gassing from carpets and paints and wood finishes cannot escape. If you run a large negative pressure in a typical house, you also risk carbon monoxide poisoning from sucking exhaust from the furnace into the living space.
> I know hospitals employ air pressure as a way of controlling for disease spreading.
They use air pressure this way specifically because construction is not airtight. If you run a negative pressure differential (which requires a pretty beefy blower to accomplish and isn't very energy efficient), you end up pulling air in from all the gaps and cracks and porous materials, which means that contaminated air is not going into all the gaps and cracks and porous materials.