According to the final post here (found using search term "prelude to a plague walkthrough"), it may be that he/she wanders off to the village & you have to wait for him/her to come back. This happens on occasion. I actually remember playing this quest a week or so ago & didn't look it up, got impatient & just cancelled the quest. I'll try to have more patience next time.
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Don't heal the sick Sims with the icons over them or interact with them until you are told to do so. This quest is very specific and after playing it again after years of not playing TSM I mistakenly healed those two with the plague (just doing my daily job tasks) and could no longer do things as the OP mentioned. So, don't heal them or diagnose or whatever, until the game tells you to do that. Do not include those in your daily tasks if it happens to tell you two Sims etc. Let that daily task go or you will not be able to complete this quest. Be careful in TSM some players ( I mean Sims) have particular roles so leave them alone.
"Games Are Not The Place To Tell Stories, Games Are Meant To Let People Tell Their Own Stories"...Will Wright.
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I can help you. Log in to Facebook and visit my FB page about the sims Medieval. Scroll down, and you'll find my gameplay of this quest from the 2. September 2014: https://www.facebook.com/thesimsmedievalpiratesandnobles