Well, yeah but no.
Sure, preponderance is the standard if it makes it to court. But proving negligence is on the plaintiff.
Negligence requires duty, breach of that duty, and causation.
That’s a helluva standard to meet without getting too far in the weeds legally speaking. Especially the last part - causation.
If you can establish the hospital had a duty to prevent the spread of COVID, and if you can prove they breached that duty, then you must prove they are the actual and proximate cause of the injury to the plaintiff. Good luck proving they are the actual and proximate cause of a virus that’s spreading through the community with impunity.
Because of the nature of viruses, it would almost certainly never meet this standard. When you file a lawsuit like this the opposing counsel is going to ask for summary judgment and to have the case dismissed for failure to state a claim.
Now it’s possible it makes it into court, but I wouldn’t bet on a judge allowing it.