I recently bought a decent phone (a shiny Samsung s4), so I spend about an hour a day looking for interesting things to install on it. Many many Google searches later and I'm now familiar with Sarah Northway's Rebuild series, a game of post-apocalyptic world-building that mobile gamers seem to love. It's a turn-based strategy game where the survivors of an undead uprising begin to build out from their base, reclaiming the area surrounding their protective cordon one building at a time. It's pitched as Sim City meets The Walking Dead, with the city's expansion bringing personal stories of survival and adventure to your little gang of un-undeads. The Kickstarter pitch is on the other side of this here protective link. Dare you go on?
You are very brave! You are just the type to led this human expansion back into the world. You decide everything about the city's expansion: where to farm, where to shore defenses, all the research and training. That's while dealing with sickness, wild animals, and the crazed fringes of humanity that remain and have turned into gangs with whom you can trade or go to war. There is also the undead.
Crucially, to own the game only costs $10 Canadian. And you can test out the previous version over at Kongregate.