Plague Inc., an excellent and hugely popular epidemic simulation game, has found its way to Android. Players gently coax a variety of virus types across the globe. Your plague starts off as a modest cough, then mutates with new and insidious forms of transmission, deadlier symptoms, and greater resistance to medication.
Plague Inc. involves a lot of finesse, since you don't have much direct control over the virus, so must simply make calculated mutations, pay attention to pertinent world events, and adapt accordingly. It's harder than you think to wipe out the entire globe; airports shut down, governments are alerted, and before long, the whole world is banding together to find a cure.
On the one hand, Plague Inc. is an incredibly morbid game, but on the other, I've always had a hard time putting it down. It's available for free with an unlockable full version with fast-forward enabled, so go ahead and check it out.