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You can't get AIDS from saliva. If it originally came from monkeys, someone must have either shared a needle with a monkey, or slept with a monkey without protection. I find both things very unlikely, and any West African will beat you up for suggesting that.
I'm more tempted to believe the virus is a mutation caused by the (now abolished) compulsory hepatitis shots in West Africa.
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If the monkey has any blood or damaged tissues in its mouth, then its bite can transfer the virus.
Monkeys suffer AIDs, too, so we know that the disease is shared by both species; a mutation in the virus is what is suggested by the evidence, and supported by most scientists. I'm not certain how a vaccination could lead to the emergence of an entirely new virus, since most vaccines use only dead viral matter, sometimes in a bacterial host...