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Can someone recommend good books on mathematical biology for self study. Especially to understand SIR models and stochastic models such as branching process. For SIR models I want more of beginner level book with explanations on how to derive the differential equations in the model and how to estimate those parameters. Also, I would like a book which explains on bifurcation diagrams.

Although I didn't read it yet, I found in anther post that "Mathematical Models in Biology" to be a good one.

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You can try to look into Mathematical Tools for Understanding Infectious Disease Dynamics by Odo Diekmann, Hans Heesterbeek and Tom Britton (Princeton UP, 2013), however, you do need quite good mathematical background to start reading it. This book includes careful derivation (and drawbacks) of the classical SIR model, and treats branching processes from scratch. It does include statistical aspects, but I do not think it has any introductory treatment of bifurcation teory.

If this book a little too advanced for you, you can try to look An Introduction to Infectious Disease Modelling by Emilia Vynnycky and Richard Whit (Oxford UP, 2010).

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A particular favourite of mine is the following

https://press.princeton.edu/titles/8458.html

It was recommended to me by a supervisor of mine and has been of great use. From a mathematics perspective it has primers throughout the book, making it easier to grasp the concepts discussed on the biological side regarding model construction.

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