I am a little ignorant on the point I am about to make, but is it realistic to believe that a plague could just spontaneously erupt out of nowhere? Maybe it could, but then maybe it was just already there, I guess.
Now to my real questions before I begin. If this fictional island is so “dead” as you call it, largely devoid of any plant life (herbs), animals, and any other resource (Is this place basically a floating rock?), it sure is convenient that I not only had exactly the specific resources I needed to concoct the cure, but also that there was enough of the resources needed to make enough cures for all of the people suffering from this dreadful plague from nowhere. These facts, and you also ask us to assume that I am somehow able to even procure these preciously scarce resources without a bit of suspicion from the rest of my fellow humans on the island. These people must be so dumb that Charles Darwin might just rise from the grave to strangle me himself just for act of saving these low-totem gene pools. I am probably better of without them, right?
Oh, how convenient also that I hit an unspeakable stroke of luck by also coming across the resources needed to at least construct the makeshift lab I would need to develop this cure, and let’s also not forget that I must have come across enough animals close enough to our DNA structure (exclusively monkeys) with which to even realistically attempt to accurately test my various incarnations of the cure on. After all, since nobody knows I have the cure, I must have tested it on something, right? And, as I said before, that something must have been an animal, and probably a monkey, right?
Oh, but then I get even luckier, right? Because I was somehow able to beat even more insurmountable odds that the disease would not only affect the monkeys, but also affect them in the same way it did my fellow humans. AND…that the monkeys’ positive reaction to the cure (minimal side-effects compared to the benefits of treatment) will also be just as positive, if not more so, when injected into the humans.
But, even despite all of this, even if I get the best reaction possible out of the monkeys, I still cannot be positive the cure works on humans at all, can I? Chiefly because I could not test it on them; that is, of course, unless I had the disease, concocted the proper variation of the cure in time to test it on myself, saving my life. I better have done that quickly; apparently this disease kills you “within days”. Of course, even then I only know it works on me; that would hardly constitute reliable data of testing populations statistically necessary to even be somewhat sure the cure even works on a few people, let alone most of them.
However, despite the many ludicrous and statistically impossible factors that you ask me to assume when answering this question, I will accept your scenario at its face and answer anyway by offering up a much more likely means through which I was able to attain such a cure without anyone knowing about it. I will simply assume that the Arch-Angel Gabriel swooped down in chariots of fire and hand delivered me the full proof cure; one divinely forged by God himself on the mason stone of Thor, Gabriel dawning a sound proof cloak of invisibility, shielding him from the eyes of the rest of the island population. God was thoughtful enough to make us a cure, but not thoughtful enough to give it out equally; rather for some reason he made me sole-bearer of the cure, free for me to exploit. He was also thoughtful enough to put us in this shit hole in the first place.
Obviously, I would choose option one (release the cure), and for two reasons:
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Given there is even a somewhat functional market that has emerged, it would be in my self-interest to release the cure. I imagine that most of the people suffering from such a painful disease would be willing to give me almost any property they had just to make all their pain a suffering stop, at least for the time being (these are the ones that haven’t committed suicide yet – I assume we have no law against suicide on our little island). If this disease is actually as dreadful and horrific as you claim it to be, demand for the cure would be through the roof, especially if the alternative is increasing pain and then death. Dying people will pretty much give up everything they have if the alternative is to lose it all anyway. Because of my monopoly over the supply, as well as the gargantuan demand of those diseased and the families who rely on them, I would become wealthy beyond measure – or extremely wealthy relative to the rest of the island - and I will have done a good thing; I ended all that death and suffering, and made the island a more productive place (you’ll see why in reason number two). Pretty much so long as there is enough on this shit hole to keep me satisfied, I am good, because most of these diseased people literally gave me everything they had. Sound cold? Reason two may offer some compassionate comfort to you.
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Despite the dire scarcity of resources we live in, releasing the cure would be not only be to my self-interest, but to everyone else’s as well. More bodies means more laborers, which conveniently results in a greater and more efficient division of labor for everyone to enjoy the benefits of. Sure, there is a pittance to go around, but the division of labor makes utilizing these resources more efficient, and I would imagine that the innovation to be realized by a bunch of starving, thirsting people would be pretty impressive given the circumstances. Necessity is the mother of what? INVENTION! The better the division of labor, the more likely we are to fashion a boat to get of this damn rock, or at least venture out to find people to trade with. Let’s not forget that we can produce more nets, and gain better fishermen to tap into that seemingly unending source of food we call the ocean; how about that for decreasing animal scarcity, for ya?
I think I probably pointed out enough flaws in the premise of your story alone, so I won’t go further. The problem with scenarios like these is that, while they appear plausible if you don’t think too hard, they fall apart once you do. You find that they are so internally inconsistent that they are really impossible in the real world, which makes them good for nothing more than a bit of mental masturbation, and perhaps a good laugh. Try pitting us into a realistic scenario, and maybe you’ll get some serious answers; Hell, you and I might even learn something.