Part II Mathematical Biology resources

The Part II Mathematical Biology course is an excellent introduction to mathematical modelling of dynamical systems, and opens the way to many applications in diverse areas.

This page is work in progress, and I shall add to it as I find more interesting stuff. Suggestions are always welcome, email me.

Reference material

The Schedules define the limits of the course (specifically, a lower bound for lectured material and an upper bound for examinable material).

Examples Sheets for this and other DAMTP courses.

Books and lecture notes

• David Tong's lectures.

• Julia Gog's lecture notes.

Games/Demos

Nicky Case (https://ncase.me) has some really fun demos.

• emoji simulator simulation of epidemics

• and of the BZ reaction

• COVID-19 models

• Spontaneous synchronisation of fireflies (and here's a video of it happening in real life)

I am less talented, but made some

• Interactive demos in Python for this and various other Maths Tripos things.

Media

• Belousov-Zhabotinsky reaction demo by NileRed

Interesting papers

(Please take section titles as content warnings.)

Epilepsy

• Yang and Robinson (2017). Critical dynamics of Hopf bifurcations in the corticothalamic system: Transitions from normal arousal states to epileptic seizures

• Rinzel and Huguet (2013). Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection

• Rinzela and Ermentrout (1989). Analysis of neural excitability and oscillations. In Methods in neuronal modeling: From synapses to networks.

Drugs and addiction

• Modeling the Prescription Opioid Epidemic

• A Fast-Slow Dynamical System Model of Addiction: Predicting Relapse Frequency

• Insights from system dynamics applications in addiction research: A scoping review

• A dynamical system approach in modeling drug abuse in Isfahan Province

Homelessness

• A model for housing allocation of a homeless population due to a natural disaster