books for beginners in research in mathematical biology
Probably the best contemporary book taking a broad view of mathematical biology modeling is Otto and Day's 2007 book A Biologist's Guide to Mathematical Modeling in Ecology and Evolution published by Princeton University Press.

There are also a number of books that focus on more specific areas e.g. mathematical population genetics, ecological modeling, infectious disease epidemiology, etc. But without knowing which areas of modeling interest you it is difficult to recommend at this level.