If I understood the hints well, she doesn't get periods. Perhaps it was a side effect from the plant she ate as a kid.
SPOILER SPOILER SPOILER SPOILER
So from what I've garnered the only way for someone from another bloodline to give birth to a taran child is for them to ingest a specific flower since very young, which would essentially "purify" their bodies and stop their periods. In the books its revealed that Vivian would often ingest a random plant that grew around the castle (back when she basically lived alone as a princess) which is why, the first time she married she could never have children (with fat, old, abusive dude). In the "original" storyline, she would eventually run into an old doctor (the very doctor we just met, the Tarzan's doctor) who would identify why she was infertile and give her a concoction to return her body to normal, thankfully by then she would've been too old to have children.
However, the taran doctor never fully explained to her why she had been infertile, so the Vivian of today doesnt know that shes actually the perfect "vessel" to host the Taran bloodline. So, long story short, she probably is pregnant and both of them are going to be REALLY shocked soon once this all comes to light.
did you read the novel??? where do you read it? ヾ(☆▽☆)
could you please tell me the chapter in which vivian gets to know she's pregnant???
I think shes pregnant maybe count metten was infertile so she never got pregnant or the stress cause her body not able to form life