# References

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, https://itunes.apple.com/us/book/basic-pharmacokinetics/id505553540?mt=11 **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.