My internet connection + puke's new post just lost my long list of references and documentation, but I got to retype it...
We begin with why Disease is important to expeditions:
Disease played a major part in how expeditions worked out. The de Soto expedition was following the failed Narvaez expedition. The Narvaez expedition was a colonization effort.
http://en.wikipedia.org/wiki/Hernando_de_Soto#1539_to_early-1540_in_Floridahttp://en.wikipedia.org/wiki/Narv%C3%A1ez_ExpeditionThat expidition resulted in the devistation of the Missippian Culture. (The Missippian organizational structure was already destroyed by famine prior to the arrival of the Europeans. This just killed off everyone who remembered it, so that the order that survived was destroyed. The true extent of what occured really cannot even be imagined, since there is nothing to compare it to. A good example is this though, According to the de Soto expedition, the Coosa Super-Chiefdom commanded a vast area in Alabama, Georgia, Tenessee, and North Carolina. The Coosa had many chiefdoms under them, with a population in the tens of thousands. Then it disintegrated. The Cherokee took much of the land the Coosa lost to disease. The rest became part of the Muscogee Confederacy (eventually). This was a real concequence of expeditions. For example, we look at the expedition that de Soto was involved in just prior to the one he lead and died on...
The Conquest of the Incan Empire
http://en.wikipedia.org/wiki/Francisco_Pizarro#Expeditions_to_South_Americahttp://en.wikipedia.org/wiki/Spanish_conquest_of_the_Inca_EmpireIn 1528, the king of the Inca and the designated Heir died to smallpox. This may have come from Pizarro's expedition that went close to the Inca border, or it could have been from a different source. Reguardless, the Inca Empire was the only group in the Super-Contenent of America to have extensive road systems. At first you may think "Who cares", but disease can prevent travel. Moving fast allows disease to spread before it is even noticed. So, the road network probably turned into a very deadly tool used by Smallpox.
There was 90%+ fatality rate to native villages that became infected with smallpox. This resulted in 2/3rds of the Blackfoot population to die on the great plains in 1837. Imagine what it looked like in the Inca Empire, where people traveling between their villages was probably quick and easy. I'd believe 75% casualty rates pretty easily. Keep in mind that in the 1526 Expedition, when he saw the tribe that the Inca conquered, he was afraid due to their numbers and attitude. Now imagine the people that must have conquered them. He had more than 160 men with him at the time, supposedly.
Yet in 1532, with less men then previously, he marched in. A lot of his success was with the audacity of his actions, but just the same, the dramatic change in opinion of the difficulty of the task probably had a source somewhere.
Cortez's expedition had it's own windfall from smallpox, but due to the nature of what happened, it wasn't as great a benefit as it was for Pizarro. Cortez had great armies of Natives fighting at his side, and the losses by the Aztecs were paralleled with losses from the Tlaxcala and other allies. Still, assuming a 30% fatality rate that EUROPEANS have when exposed to smallpox, and the fact that every person in that city probably got exposed, that city must have been choked with corpses. Keep in mind that at the time, this was among one of the largest cities in the world. Assuming a population of 300,000, that'd be 90000 people dead in 3 months. That was 1000 times the force that Cortez had. As other places show though, the fatality rate for natives on first exposure was generally significantly higher than 30%. The people in the area had a prophecy of the end of the world around this time. Imagine how it must have looked to them. This outsider overthrows the regeme at the top, and then practically everyone you know starts dying.
This doesn't do much except prove it has an impact on expeditions. But there is still the problem, how to prevent it from wiping out all the natives.
Short answer: Don't. The idea is to have the natives seem numurous when you arrive, and look as it currently looks as the natives end up ravaged by the disease.
Long answer:
It took 26 years for the disease to cross the ocean. (There are some who claim a 1507 disease date, but I've found no evidence supporting it, and some counterdicting it.)
This is because smallpox takes about 15 days to become infectous, and sometime around three months for a ship to cross the ocean. Ships are tight quarters, and so it is actually pretty difficult for an infection to not run it's course. There were some pretty sizable expeditions that came out before the disease came. This is due to the fact that once you have been infected with smallpox and survive, you are immune. Smallpox ravished Europe pretty constantly, so you didn't have a large percentage of the population who didn't have immunity. So getting a sailor infected at all would have been somewhat rare.
But let's ignore those hurdles, which would make the infection pretty hard unless you deliberatly attempted to carry it. Your next hurdle is that the people who have almost no resistance would spread it too quick. If your population X is mortal enemies of population Y, you probably don't regualrly send trade delegations into their territory. You also aren't going to send a raiding band with someone who is sick. He wouldn't be able to hold his own. As such, every place there is strife between tribes, you have a wall blocking the transmission of the disease. The ones who have it would die off and then the entire progress would halt.
Finally, there are seasons. Travel in winter is harder than in the summer. As such, during the winter you'd have infected villages die off without spreading it. It might be bouncing around a little still, but not as strongly.
Not every village has to trade with their neighbors twice a month. As such, it is entirely possible that a trade delegation from neighboring villages might not even be exposed.
Of course there are some strong countering forces to those actions too. Smallpox-infected clothing and blankets, for example. There is also the extensive trade network that the natives have. There might be a neutral group on the side of each of those two belligerants which infects them both and keeps spreading it. It's estimated that the disease could have reasonably spread 200 miles before someone got sick, resulting in a situation where the disease might have been spread across the entire supercontenent in no more than a year.
Likely in some form it was spread across the contenent by the early 1600s, probably more than once in fact.
If you have a large starting population and give survivors immunity to smallpox, and only have it transmit via active infections, you could make a pretty good model that, combined with models that cause the natives to have strife with each other and colonize and populate places on their own, creates a situation that could allow clever expeditions with very small forces to loot an area and then return to see friendly allies took over the countryside. Perhaps even people that you convinced to be loyal to the king of Spain. Or maybe you might loot an area with help of your allies only to come back later to learn that your allies were defeated, since they were severely weakened by smallpox, and now your safe area has become too dangerous to explore.
But enough about disease. If it happens, it'll happen. I am certain that if you model it right and start with huge native populations, it should come out pretty evenly.
On to puke's addition...
1490s was early expeditions and establishing footholds
1500s were identification of primary native powers
1510s were the initial assaults of the native powers
1520s were looting expeditions
1530s were colonization expeditions of spain and portugal and final conquests, and french explorations.
1540s were exploration expeditions
1550s were when the other powers started exploration expeditions
1560s was when you could reasonably consider to be the period of colonization.
Everything before the 1520s would have lots of natives. Times after that would have fewer.