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explain how the specific immune response differs between two patients who have been infected with the same virus. patient a was previously vaccinated against the virus, while patient b has no previous exposure to the virus.

For Patient A since they have been Vaccinated, the immune system will already know what the virus looks like and train itself to combat that specific strain of infection and be able to combat it immediately.
Person B will have to go through the process of the white blood cells combating, T cells, B cells, Macrophages, and getting sick since their body doesn't know how to combat it, after the infection the body will keep a save of the strain for later use.