The majority of science about fasting and vaccination centers around Ramadan-style fasts, afaik. https://www.goodrx.com/blog/covid-vaccine-ramadan-fasting/ for example.
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It sounds like a ramadan style fast is thought by some to improve immune response, but it’s not clear. I’d suggest doing Intermittent Fasting in the weeks between your two doses if you are at all worried about it impacting your immune response.
This article does explain pretty good why exzended fasting is a bad idea. Also it got some medical references to check below the article: https://www.zerofasting.com/fasting-covid-and-vaccines-everything-you-need-to-know/
I have autoimmune. The vaccine triggered a flare up of my symptoms. I am doing intermittent fasting for 16 hours a day. I am eating AIP no sugars, grains, nightshades or eggs. I drink bonebroth and tea in the morning. A shake at lunch of plain coconut milk and fruit. Then eat a normal meal for dinner. After the first day I felt great and slept deep. Sencond day my symptoms came back after eating grassfed steak cor dinner. I feel bad. Is it just the vaccine doing its thing. I am worried about the next dose.