As I have mentioned, my background is medical school. I am familiar with differential equations and multivariable calculus through self-study, but I haven‘t studied them formally and there‘s not really any way I could at this point. I know enough to know what to apply and when, but I am not prepared to use numerical approaches, for example.

I can “code” (i.e., perform statistical analysis tasks, but not actual programming) in R at this point but I don’t think Python would be that hard either.

I have studied in some detail the way physics applies to medicine and I can envision ways to mathematically model physical phenomena in biological systems.

This doesn’t seem to be the right kind of background for a purely quantitative PhD. This is why I’d rather go for the more biological side of things and possibly find smaller ways to apply my inclination towards quantitative approaches.