# Final thoughts and acknowledgements

# Summary

You have reached the end of this open education resource on introducing mathematical biology – well done! In every chapter we have given 3 key takeaways to remember. What are 3 key takeaways from this whole book?

Key Takeaways

- We can build mathematical models for biology or medicine by considering the mechanisms that will increase or decrease the whole or parts of the population.
- We can apply a range of tools from dynamical systems – from explicit solutions, to qualitative analysis, to computational simulations – to infer how populations will change over time and under different parameter regimes.
- Even simple models can provide us with very useful insight into biological and medical systems.

# Further study

I hope that this open education resource has proved useful to someone out there. If anyone ever finds themselves having read to this point and thinking they have found it useful, please do feel free to let me know using the anonymous feedback form, as this helps me understand how the textbook is being used.

I also hope this textbook might inspire you to further study, whether within a specific area of mathematical biology or medicine, or more generally in mathematical modelling. This has been a bit of a whistle-stop tour of investigating questions from across biology and medicine using ordinary differential equations. As stated at the very start of the book, this is just one method for approach modelling questions, and the more mathematically or computationally adventurous amongst you will find many different technical approaches out there. Similarly, the biological questions are by no means limited to the topics covered here. As a first step to further study, you might find it useful to browse some of the references for some more in-depth study of particular subjects. You could also search for mathematical biology research groups at a nearby university or research body (a quick plug: click here to go to the webpages for our own research group) – on the whole we are a friendly bunch and will generally welcome enquiries from those interested in pursuing further study.

# Acknowledgements

It is a cliche, but this work would truly not have been possible without the support from a number of wonderful people. Firstly a huge thanks to **Oscar Devine-Wright**, who worked as an assistant in preparing the book and undertook many helpful activities, including producing the wonderful hand-drawn figures.

I also picked the brains of my colleagues in the mathematical biology research group at the University of Sheffield many times during the process. An extra special mention goes to **Nick Monk**, with whom I taught the *Mathematical Biology* module at Sheffield for many years, the content of which formed the backbone of this book. Further thanks go to **Alex Fletcher** and **Jonathan Potts** for their helpful thoughts and feedback. I’d also like to thank my erstwhile PhD students who read parts of the content and gave useful feedback, **Prerna Singh**, **Megan Oliver**, **Charly Pain** and **Ryan Grossman**.

I must thank the **Open Education Resources** team at the Unviersity of Sheffield Library. Importantly, the team provided me with funding that allowed me to focus on developing these materials in early 2023. I’d particularly like to thank **Helen Moore** and **Maria Mawson** for their support in every stage of the development. I must also thank the **UK-US Fulbright Commission** for awarding me a visiting scholarship in 2021, during which the idea behind this textbook started to form.

I’d like to thank members of the **Mathematics and Statistics Digital Accessibility Working Group**, especially **Jenny Hughes**, as it was conversations as part of this group which first led me to exploring the world of Open Education Resources and online materials. I’d also like to mention the team behind the **Jupyter Book** initiative, as this was the first platform I used to create free, online content for my lectures and they unwittingly built my knowledge and confidence of how to develop online materials.

# About the author

I am a lecturer in the School of Mathematics and Statistics at the University of Sheffield, specialising in mathematical biology. I obtained a BSc Mathematics and Philosophy from the University of Durham in 2005 and an MRes Mathematics in the Living Environment from the University of York in 2006. My PhD was titled *Modelling the evolution and coevolution of host defence* under the supervision of Prof Mike Boots in the Animal and Plant Sciences department also at the University of Sheffield. I have been teaching undergraduate and postgraduate maths courses since 2013 and I was a Fulbright Scholar in 2021.

My teaching focusses on mathematical modelling, guiding students through how to build and analyse models for real-world systems. I place a strong emphasis on embedding equity, diversity and inclusion into all I do and am passionate about encouraging and supporting students from minoritised groups to succeed in mathematics.

I live on the outskirts of Rotherham with my wife and children.