What's the risk from dead pathogens - immune overreaction? It's a screwball idea, but I wonder if there might actually be health benefits to reliably killing p

What's the risk from dead pathogens - immune overreaction? It's a screwball idea, but I wonder if there might actually be health benefits to reliably killing pathogens without filtering them out of the air - sort of like low-dose inactivated-agent vaccines for everything you would have actually been exposed to otherwise.