I think of "refereeable" as meaning "a reasonable editor at some non-predatory journal somewhere could consider this paper worth sending out to a referee".
With your paper, the obvious red flag for me is that it only cites one reference - it makes no real attempt at all to connect your work to existing literature. On that basis alone, any journal would desk-reject the paper without sending to a referee; it would be a waste of a referee's time to review a paper in that form. So I think the arXiv moderators are literally correct in calling it "unrefereeable" and in rejecting it. (And of course, it can't help that there is undoubtedly an uptick in crank papers on epidemic modeling right now.)
It's unclear at first glance whether you are giving a new exposition of existing results, or discussing new interpretations / consequences / applications, or whether you are presenting genuinely new results. Any of those things would be acceptable for arXiv (the first a little bit borderline but still usually okay), but you need to make clear what's what.
So that's the obvious first way to improve the paper: include a proper literature review, and put your work in context.
Other than that, the paper certainly appears to be real mathematics (though I'm no expert in that area). You might be able to have someone in the field (maybe one of your endorsers?) look at the paper on the same basis: if they were a journal editor, would they send this paper to a referee?
When you get it to that point, I think it would be completely reasonable to resubmit to arXiv. It sounds like you ought to contact the moderation team first, probably with some acknowledgement that the initial version was unacceptable but that you have improved it now. It's possible that it will be rejected again, but if so it would be reasonable to appeal at that time.
Also, I note that you don't include any contact info in the paper (at least not in the HAL version), nor mention any affiliation. Contact info such as an email address is generally important. And if you have an affiliation with an academic institution, company, or other known organization, it would not hurt to mention it (get your employer's consent if you need it, of course). Ideally your affiliation should not be a consideration in the preprint's acceptance, but it is something that people will notice.