I'm on the Mathematics faculty of an Australian university. The way it seems to work at my university, and maybe at other Australian universities as well, is that a PhD applicant is accepted only if there is a faculty member committed to acting as supervisor. So it seems to me that the indicated strategy is, when applying to the program at University X, to look at the faculty at University X, see if anyone there is working on something you could imagine being interested in, quickly learn enough about that area to write a few sensible sentences about it, and proclaim that you would be happy to work on that topic or on such other topics in Math Biology as people at University X might want you to work on.

It does seem strange to me that a beginning postgraduate would be expected to have a research proposal - it certainly didn't work that way when I was applying to PhD programs in the US in ancient days - but I guess you have to go with it.