no it doesn't absolutely mean you are not infectious, there are tons of wrong things told by doctors and some by researchers on previous years, the tests to monitor infection are:
quantity of all antigens and antibodies hbsag enclosed which is rarely available in US but widely available in europe and asia, hbvdna pcr real time (detects 1-10iu/ml or <20iu/ml according to assay used), when hbvdna is und in the blood it is und in semen too but you are still contagious especially through blood
hbe positive is bad because there is more damage, more cccdna, more virus generally, hbeab positive and hbeag neg is better because there is inactive or low replication but you are still infect, even on hbvdna und there is hbv replication and you are infect, the test of good immune control and clearance of virus is hbsag neg and hbsab pos, but the blood can still infect others even with hbsab for decades and some very low hbvdna can still be found although harmless for you
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