Interesting examples of models
Biology is a large field of knowledge! As you give examples drawn from population biology (logistic population growth and Lotka-Voltera models), I will assume you are mainly interested in ecology and evolution.

For analytical models used in ecology and evolution, I highly recommend the book A Biologist's Guide to Mathematical Modeling in Ecology and Evolution by Otto and Day. The book assumes a relatively low level of knowledge in mathematics from the reader and walk the reader through most of the most iconic models in ecology and evolution, their analysis and interpretation. The mathematical tools used in this book include linear algebra, equilibrium analysis, analysis of cyclic behaviour, Markov chain and esp. birth-death processes, diffusion equations, probability theory and stochastic models, approximation theory, class structure models (Leslie matrix and more) and, separation of time scales among others.

For books, mainly theoretical, in population genetics, please have a look at the post Books on population or evolutionary genetics?.

As you talk about the Lotka-Voltera model, you will find an intro to this model in the post What prevents predator overpopulation?.