All cities and towns of this state shall have the power to aid, establish, set up, and regulate hospitals, poorhouses, workhouses, houses of correction, and pesthouses anywhere in the county in which the city or town is situated and cause persons afflicted with contagious, infectious, or pestilential diseases to be removed to such hospitals or pesthouses as may be provided for the purpose and to cause persons who have been exposed to such diseases, or any of them, to be removed to some suitable place of detention and detained for a reasonable length of time.