The material that formed this book has been developed over a number of years as part of my teaching at the University of Sheffield, particularly in modules of Mathematical Biology, Mathematical Modelling of Natural Systems and Mathematics and Statistics in Action. This is very much a ‘standing on the shoulders of giants’ production, and I have tried my best to acknowledge the various sources that have fed into this material, either directly or through some general osmosis. For each chapter I have tried to list the works that were directly used in developing the content, and their detailed citation information is listed below. I particularly want to acknowledge the following resources that have played an indirect but important part in choosing and explaining the content:

  • Mathematical Biology by Murray – most people in the field will know this as the definitive textbook for mathematical biology teaching, and I suspect more ideas than I realise have come from this classic.
    Murray, J. (2002). Mathematical Biology I: An Introduction. New York: Springer.
  • Modelling Infectious Diseases in Humans and Animals by Keeling & Rohani – again, a bit of a classic in the more specific field of epidemiological modelling.
    Keeling, M. and Rohani, P. (2007). Modeling Infectious Diseases in Humans and Animals. Princeton University Press.
  • The Basic Pharmacokinetics e-book and webpages by Bourne – a fantastic resource for learning about pharmacokinetic models.
    Bourne, D. (2022). Basic Pharmacokinetics v1.5.5. Apple iTunes bookstore,
  • Nonlinear Dynamics and Chaos by Strogatz – there are a great many books devoted to the general field of dynamical systems, but I would argue this is by far the most accessible for an undergraduate mathematician.
    Strogatz, S. (2000). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering. Westview Press.

Further reference list

  • Anderson, R. and May, R. (1981). The population dynamics of microparasites and their invertebrate hosts. Phil. Trans. Roy. Soc,. B, 291:451–524.
  • Anderson R. and May, R. (1982). Coevolution of hosts and parasites. Parasitology, 85:411-26
  • Best, A. and Ashby, B. (2022). Herd immunity. Curr. Biol., 31:R174-R177.
  • Geritz, S. Kisdi, E., Meszena, G. and Metz, J. (1998). Evolutionarily singular strategies and the adaptive
    growth and branching of the evolutionary tree. Evol. Ecol. 12:35-57.
  • Gerlee, P. (2013). The model muddle: in search of tumor growth laws. Cancer Research, 73:2407-2411.
  • Goodwin, B. (1965). Oscillatory behavior in enzymatic control processes. Adv. Enzyme Regul., 3:425–428.
  • Hahnfeldt, P., Panigrahy, D., Folkman, J., Hlatky, L. (1999). Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Research, 59:4770-4775.
  • Hernandez-Vargas, E. and Velasco-Hernandez, J. (2020). In-host mathematical modelling of COVID-19 in humans. Annual Reviews in Control, 50:448-456.
  • Perelson, A. and Nelson, P. (1999). Mathematical analysis of HIV-1 dynamics in vivo. SIAM Review, 41:3-44.
  • Yin, A., Moes, D., van Hasselt, J., Swen, J. and Guchelaar H-J. (2019). A review of mathematical models for tumor dynamics and treatment resistance evolution of solid tumors. CPT Pharmacometrics Syst Pharmacol., 8:720–737.


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Introducing Mathematical Biology Copyright © 2023 by Alex Best is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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