I think that traditional "quest" model wouldn't really fit the player driven nature of Day Z properly. In my humble opinion a better idea would be to add more back story to the world, seed it out onto the map in one form or another then and let the players discover it for themselves. By this I mean flesh out the who's, why's, what's, where's and when's of how the infection came into existance, how it got to chernarus and how the goverment and local population responded to the outbreak then spawn the notes/letter/files etc that contain this information across the map either randomly or in set places. Something along the lines of having a file about Patient Zero drop in a hospital somewhere for people to find, randomly spawn a military convoy carrying water/soil/air samples that shed light on the origins of the infection/how it it transmitted, the ability to find written orders in military tents that show how the army was told to respond to the outbreak. There is whole host of things you could do and the majority of it would be fairly simple with the current game resources. This approach would put something in place for people who want more out of it than just surviving without really altering simulator style nature of the Day Z experience. As a though this would also tie in nicely with the player factions and player made bases. You may find those infection samples but down the line they may need equipment/ a player with that equipment to analyze it etc. TL;DR: Dont have traditional quests but seed more back story about the infection around the map. Your "quest" is now to find out what happened.