Is it permissible to kill a patient with rabies after losing hope of their recovery and their posing a threat to others?

It is not permissible to kill those afflicted with deadly infectious diseases such as rabies and leprosy, due to the sanctity of life. However, they must be isolated in a special place (quarantine) to prevent their mixing with people. Indeed, there is a command to flee from the leper, and Ibn Uthaymeen reported the obligation to isolate lepers. The Malikis, Shafi'is, and Hanbalis held that a leper should be prevented from mixing with healthy individuals unless with their permission, and this ruling applies to other infectious diseases.