With each dose, you began to build immunity. For complete immunity, three doses are given. You should have the full immunity within a month. So far, after receiving the three doses, it is believed to give long term immunity, but if you work in the healthcare field, it might be wise to check your titer in several years. I know when I got my Hepatitis B vaccinations, after my last shot they checked my titer a month later to make sure it took.
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