I know a person who had mild symptoms, was tested positive in the PCR test and did not have any antibodies 6-8 weeks later. He then looked into the subject deeply. His conclusion was: You can develop antibodies after infections, but not everybody does. Also: a lack of ABs does not mean that you aren't immune. After all, many people were asymptomatic or showed only mild symptoms without any ABs... There is the second, much less known immune system called cellular response, which seems to play a strong role in this disease.