There si no sleeping, only resting.

From the manual:

Resting
The game tracks each survivor’s fatigue. As they start to tire, you’ll see a note on the reverse of their portrait indicating how tired they are. When they’re exhausted, they’ll stop whatever they’re doing and rest. When resting, survivors can’t be given orders (except for moving between locations) and won’t perform any idle activities. However, they may find themselves embroiled in some events, dilemmas and combat.
Of course, survivors may choose to rest at inopportune times. Ordinarily, you don’t have control over resting, unless your survivors are in a hotel. This special location will allow you to issue a Rest order.

Injuries
It’s highly likely your survivors will become injured, either by zombies, another survivor, or some other special event. Injuries are serious and should be treated as soon as possible, otherwise they may develop into an infection, cause fevers, or at the very least, reduce the survivor’s capabilities.
Injuries require the right medication to treat an injury (see Orders – Treat injury). Once treated, the survivor may still be affected by the injury, but the effect will be less than if it were untreated.
Injuries are classed as contusions, concussion, lacerations or broken bones. You can view a survivor’s treated and untreated injuries by right-clicking on the portraits in Planning view.