Once again, i wasn't denying the filth of cities--and this discussion was motivated by Hobbes' charge that life in a state of nature was, among other things, nasty. I don't think you'd be doing much bathing in streams, etc., for most of the year during the ice ages. Also, for parasites such as fleas and lice, you need not only to bathe, but to put on clean clothing afterward. Not only would washing clothing made from animal skins be difficult, but it would tend to ruin the fabric of your garments. Chiggers, as you know, burrow into the skin--bathing wouldn't help much. The main thrust of my remarks was that the parasites of wilderness would be constantly renewed. Get rid of the fleas, and you'll pick up a new load the next time you go out to hunt or forage.
As for public health systems throughout history, the evidence is generally lacking. If archaeologists don't find it, it's unlikely to show up in written records. From what evidence we do have, it was spotty--so few good examples, where there is any evidence at all. Public baths were always one of the best measures, because heating water is expensive of fuel, and the Roman system was efficient in that regard. Public baths were also common among the Russians. We know this because western diplomats would comment on it in their correspondence--they found the thought disgusting and the people who availed themselves of it promiscuous. (I doubt that last allegation--i don't think there would have been a lot of promiscuous behavior when one goes out into frigid weather after having bathed.) There was a great irony in the Roman system, though. They brought water to cities on aqueducts, and they used soft lead pipes. That was because soft lead can just be rolled around a dowel rod, and then soldered quickly and easily. If a section of pipe blows out from the water pressure, it can be quickly replaced. But that also meant the population was exposed to chronic, pernicious lead poisoning, which, bluntly, makes people stupid and crazy. Looking at the history of the later empire in the west, that seems about right.
In his history of the English-speaking people, Churchill characterizes the middle ages as a period when the lights went out all over Europe and people stopped bathing. It is certainly true that "authorities" in the middle ages advised against bathing, alleging that it weakened the body's defenses against disease. (A very strange notion to us, as we tend to associate dirt with disease.) Renaissance Italy went through a fad for city planning, and providing clean water for drinking, cooking and bathing was as simple as renewing the Roman aqueducts, and waste remove meant building sewers such as the Romans had used. Public baths, though, were not popular, and in a population which had previously not bathed regularly, i can see why. Clean clothing was a big problem, too. People in Europe wore wool, and washing it is a pain, because it tends to shrink, which means that it has to be blocked while it dries out. Generally, a manor would provide a new set of clothes to the serfs once a year.
The biggest problem with the spread of disease was manure and offal in the streets. That's why i commented earlier on the automobile. When trucks began to deliver goods to cities, and horses began to disappear, the incidence and prevalence of disease dropped dramatically. As this coincided with the advent of other public health ideas, eliminating offal became an issue of legislative reform. The old English word for a slaughterhouse was shambles, so it is small wonder that shambles has come to mean a mess, a confusion. In rural areas, moving the livestock out of the house, and piling the manure a goodly distance from the house helped--but even well into the 20th century, rural areas were known for the rapid spread of disease. You don't get a lot of public health inspectors in villages.
Parasites, though, have always been with us, and likely always will be. Lice were a big problem when i was in Korea, although i suspect they've licked that one by now. But public health measures need constant vigilance. The recent resurgence of bed bugs is a good example of what happens when people become complacent.