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  • Mathematical Biology
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Summary Mathematical Biology — Complete Module Revision Gu

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12 pages
2025/2026 Written for academic year
Institution
The University Of Edinburgh (ED)
Course
Mathematical Biology
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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.

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Mathematical Biology
Complete Revision & Study Guide

A topic-by-topic guide spanning population dynamics, bifurcation theory, predator-prey
systems, excitable systems and oscillators, epidemiology, and spatial models and travelling
waves — with full derivations and worked examples throughout.



Original study notes — independently written summary and explanation

, Contents

• 1. Single-Species Population Models
• 2. Bifurcation Theory and Harvesting
• 3. Predator-Prey Systems and Limit Cycles
• 4. Excitable Systems and Oscillators
• 5. Epidemiology and Immunology
• 6. Spatial Models and Travelling Waves

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September 21, 2026
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2025/2026
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Browse related subjects

Subjects

  • mathematical biology
  • population dynamics
  • logistic growth
  • spruce budworm
  • cobwebbing
  • period doubling
  • chaos
  • bifurcation
  • saddle node bifurcation
  • pit
  • delay differential equations
  • discrete population models

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