Most bacterial and viral diseases, you develop immunity to them once you get them. This is perfectly clear once medicine is developed enough to reliably identify diseases, which admittedly happened amazingly late iOTL. From there, vaccines are obvious. Can vaccines be delayed a century or two? Probably.
But once you've got germ theory established...
The only way to avoid this is with a massive slowing down of knowledge, so vaccines were the least of your changes, or with an evolutionary change so most diseases we're protozoan (like malaria), or massive complexes of related, but non cross immunizing strains (like flus and colds). But that kind of evolutionary PoD goes in the ASB sub forum.
So. No, i don't think what you ask for is feasible.