Oh, sure it's oversimplified. And certainly diseases do move along trade routes--yet most still have their origins in Africa. For example, almost all mosquito-borne diseases are from there--the Latin American versions were imported along with the slave trade, and of course mosquitoes don't reach significantly above or below the 20 degree line (until lately--tropical diseases carried by mosquitoes have been spotted in Italy in recent years, probably thanks to climate change). Parasites, too, are mainly of African origin--their dual host life cycles means both hosts must be present and have BEEN present for long enough to allow the parasite to evolve. Malaria, schistosomiasis, guinea worm, trypanosomes.... Pathogens with animal reservoirs, like the hemorrhagic fevers, don't move outside the area of their animal hosts. And many pathogens that are exclusively human-to-human today came originally from Old World monkeys, including HIV.
Think of it this way: for a pathogen to kill its host is bad business; the pathogen also dies. So pathogens that kill humans usually have jumped from an adjacent animal species that DOESN'T get seriously sick, or else they have such a large pool of hosts to infect that it doesn't matter if they kill a lot of them.
Such is the case with diseases with no animal reservoir, such as measles, polio, smallpox, cholera. (Interestingly, of the viruses, the nearest relative is always from a herding animal, though.) Measles, with its 25% mortality rate, requires minimum populations of ~200,000 people. The population has "herd immunity"--the disease is endemic to the human "herd," but can't spread
willy-nilly because of widespread immunity. If infected, death is
still likely, but the population is large enough to withstand that and
still spread the virus. Smaller populations won't survive such
catastrophe--and thus, neither will the pathogen, because it's got no
alternative hosts.
Clearly, civilizations can withstand diseases like this, because if they couldn't, they (and the disease) would die out. But they aren't found in small populations, and no such constraint is imposed on diseases that can be maintained in other hosts and sometimes skip over into humans. Those are mainly found in tropical areas, but less so (natively) in Latin American or Asian tropical areas.
Further, almost all of these human-human diseases have their nearest relatives in cattle or pigs, so develop as a consequence of animal herding. They were unlikely to be carried into the New World by the original Native Americans because of the changes in climate that must be crossed for such migrations (see Jared Diamond on this one).
And natural history aside, of course, many of civilization's infectious diseases cluster in Africa today because of lack of infrastructure for vaccination (requires refrigeration) and sewage systems, which can be linked to the other problems described in my post.
Let's see, further reading....I could throw out a couple of textbooks, but it'd take considerable time for me to dig up papers. I'll see if I can get to it....