In the modern age, we have medicines, quarantine, and sanitation, so housing many sick people in one building without everyone catching what everyone else has is feasible. How did they get around this centuries ago? If they didn't, then why did they construct hospitals if they were so innefective?
"Hospitals" in the Middle Ages weren't just for sick people - some operated like hotels where poor and/or sick pilgrims could stay for a night. Some hospitals were completely secluded and meant for lepers. Some were modeled after religious communities where "patients" had to dress in uniform and go after particular forms of conduct.
The idea of a hospital as we know it modernly was only nascent in the Middle Ages. The majority of people who became sick either sought out herbal remedies or had a doctor go to their home.