Uh, sure it spreads in Paleo world, fairly rapidly.
skip the medical advancement.
Our knowledge of disease and prevention and quarantine, as opposed to theirs culture of superstitions, is very advanced and people just plain know to practice good hygiene.
And no, there are not several legitimate ways(vague) for it to transmit.
It is transimitted by body fluid.
That is you must provide an entrance for the fluid to enter our body.
touch a drop of the virus, wipe your eyes, eat dinner, whatever and you might very well get infected.