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Citizen's health is affected by their diet - the number of food types they have available to them. The more food types they have access to, the higher their health will be. If a citizen's health is low then they can use medicinal herbs, harvested by an herbalist, to increase their health.
Health is essential to the prevention of disease outbreaks. When diseases do occur, hospitals can be used to keep the disease from spreading and reducing the chance of death.
The more unhealthy a citizen is, the longer they will idle for - having very unhealthy citizens will lower their effectiveness at their jobs.