Healthiness: A similar approach to CIV4's is a good model to replace CIV6's Housing, that can work by itself without a pandemic disease mechanic. Technologies, buildings, policies and resources with bonus for Healthiness fit perfectly like many "requeriment" systems in CIV.
Disease: Trigger epidemic/pandemic when players fail to provide the fundamental level of healthiness is very similar to revolt from low happiness/loyalty or disaters from global warming. The probability element for disease should not be a concern if it is locked to be possible only under the worse level of insalubrity.
This is not a punishement from nowhere, it icould be the not immediate result from let a city decay for several turns. I mean you would need to ignore healthiness upgrades, fall some levels, have an alarm of the problem, then being some turn at the worse to finaly unlock the percentage chance to produce a disease and if you are lucky it could take some turn to pull out the actual disease. Then emergence of the disease would be announced to players so others could take measures like quarantine to reduce the spread and effect of the disease.
Medicament: About this I think is too complex to have resources and great people specialized to deal with disease or healthiness. I mean, of course it would be nice to have some resources with bonus for healthiness, but these resources should be just some of the resources that happen to have a health bonus between their others affects.
Now there is a think that could works and is linked to both
Science and
Diplomacy. What if at late game after the proper technologies like Vaccines, Antibiotics and Genetics players could develop treatments/cures for diseases. For example:
1- Eras before a seriously unhealthy Danish city produced the "Copenhagen's Plague", this disease already turned into a minor malus for cities where it spread.
2- Later a player put its science research queu to investigate a Treatment/Cure for this disease (I have the idea of use Science research queu for others thinks beyond technologies, like expeditions, crop varieties, academic grants, etc.), once achieved this cure the player can use it for...
A-
Patent, earn X amount of gold from every city with the diese in exchange to remove it.
B-
Donate, send your cure for free to every nation of the world, of course these would give you great diplomatic reputation.
C-
Weaponize, of course a serious evil and dangerous thing to do, but CIV allow you be "nuclear Gandhi haha-hihi"
If the last one is too much the second one is still a chance to let us think about something both more positive that real pharmaceutical politics and usefull in game for diplomatic victory.