S.D. Codified Laws Ann. § 34-1-17

Authority.The Department of Health may adopt and enforce orders and rules necessary to preserve and protect the public health and may regulate, controland, in proper cases, prohibit and suppress: the treatment in hospitals and elsewhere of persons suffering from communicable diseases, the disinfection and quarantine of persons and places in case of such disease, and the reporting of sickness and deaths therefrom.

S.D. Codified Laws Ann. §§ 34-22-5

Penalties.Every person who intentionally exposes himself or another person infected with any contagious disease in any public place or thoroughfare, except in his necessary removal in a manner not dangerous to the public health, is guilty of a Class 2 misdemeanor.