No it is not harmful to humans. This virus like most others others like it only infect plants. It is transmitted by aphids. So it survives inside of them but doesn’t replicate.
In watermelons it damages the new growth, especially the leaves. This reduces the plants ability to phosynthesize sugars and stops fruit production.
PRSV doesn’t immediately kill the plant. It kills it slowly over quite some time. It replicates in the growing point of the plant. This conveniently is the same location where aphids feed.
The aphids then transfer the virus to a new plant. Plant viruses have a wide range of host species and they move around with their vectors.
For more information, Here is an excellent write up on the virus.
https://www.apsnet.org/edcenter/disandpath/viral/pdlessons/Pages/PapayaRingspotvirus.aspx