Harzel
Adventurer
Range: Touch
Your touch inflicts disease. Undead and constructs are immune to this spell. The target gets a Constitution saving throw against your spell save DC. On a failure, you afflict the creature with a magical disease of your choosing from the list described below. The effect of the disease occurs immediately. The disease is magical and cannot be cured by mundane medicine. If magic is used to cure the disease, and a spell slot of lower level than you used to cast this spell was used, the healer needs to make a spellcasting check against your spell save DC. Failure means the magic was ineffective in curing the disease.
At the end of each of the victim's turns, the target makes a Constitution saving throw. Success means the disease is shaken off (cured). When and if the target fails three saves, no more saves are granted - the disease lasts for the full duration of the spell, and furthermore the target becomes contagious: each hour or part thereof spent in close proximity with the target means a creature is afflicted as if you cast this spell on it.
Given your modification that a single successful end-of-turn save cures the disease, I think I would favor neither requiring an attack roll nor granting a save when the spell is cast. That ensures one round of effectiveness, which makes it a bit more in line (IMO) with the half-damage-on-failed-save that most other spells have.