Summary Mathematical Biology — Complete Module Revision Gu

Mathematical Biology — an applied mathematics module covering the mathematical modelling toolkit (bifurcation theory, phase-plane analysis, perturbation methods, and PDEs) applied across an exceptionally broad range of biological systems. Written as a complete, restructured revision guide (not raw lecture notes) — organised by topic for efficient exam preparation, covering the full syllabus in 12 pages with full derivations and worked examples throughout. Index of topics covered: 1. Single-species population models (logistic growth, spruce budworm, delay equations, discrete models and chaos, the Allee effect) 2. Bifurcation theory and harvesting (saddle-node, pitchfork, transcritical bifurcations; maximum sustainable yield) 3. Predator-prey systems and limit cycles (Lotka-Volterra, Poincaré-Bendixson theorem, competitive exclusion, Rosenzweig-MacArthur) 4. Excitable systems and oscillators (cooperative enzyme kinetics, the Brusselator, Van der Pol oscillator, FitzHugh-Nagumo model, Fenichel's theorem) 5. Epidemiology and immunology (SIR model, epidemic threshold theorem, R0, herd immunity, HIV dynamics) 6. Spatial models and travelling waves (diffusion, Fisher-Kolmogorov equation, chemotaxis, the Nagumo equation, rabies spread) This guide includes full mathematical derivations (not just definitions) for landmark results across the module — including the exact closed-form travelling wave solution for the Nagumo equation, the period of the Van der Pol relaxation oscillation, the muskrat invasion spreading-speed formula, and the minimum wave speed for a rabies epizootic front. Suitable for students studying mathematical biology, theoretical ecology, epidemiology, or applied mathematics modules with similar content.