- Preface
- 1 The Origin of the Travelling Wave Problem
-
2 What a Travelling Wave Solution Is
- 2.1 A Typology of Travelling Wave Profiles
- 2.2 Heteroclinic and Homoclinic Orbits
-
3 The Fisher-KPP Equation as a Worked Example
- 3.1 Nondimensionalisation
- 3.2 The Travelling Wave Reduction
- 3.3 Existence, Speed Selection, and the Wave Profile
-
4 From the SI Model to the Fisher-KPP Equation
- 4.1 From the Non-Spatial SI Model to the Spatially Explicit SI Equation
- 4.2 Reduction to a Single Equation
- 4.3 Biological Meaning of the Boundary Conditions and the Wave Speed
-
5 The SIR Travelling Wave and Basic Reproduction Number
- 5.1 The SIR Model and Its Travelling Wave Reduction
- 5.2 Boundary Conditions, Equilibria, and Linearisation
- 5.3 The Minimum Wave Speed and the Condition for Endemicity
-
6 Births, Deaths, and the Endemic Travelling Wave
- 6.1 The Vital-Dynamic SIR Model and Its Travelling Wave Reduction
- 6.2 Boundary Conditions, Equilibria, and Linearisation
- 6.3 The Minimum Wave Speed and the Condition for Endemicity
-
7 The Travelling Wave Framework and Its Extensions
- 7.1 Extensions and Modifications Within Reach of This Framework
- 7.2 What the Method Offers
An Introduction to Travelling Wave Solutions in Reaction-Diffusion Systems
A Foundation Course in Epidemic Diffusion Models
This book is 85% completeLast updated on 2026-07-30
How epidemics travel as waves, from Fisher-KPP wave existence and minimum speed derived via phase-plane analysis, and then tied to disease spread and persistence.
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How epidemics travel as waves, from Fisher-KPP wave existence and minimum speed derived via phase-plane analysis, and then tied to disease spread and persistence.
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About the Author
Abdurrahman Tukur
A master's student in applied mathematics specializing in disease epidemiology modeling, a zbMATH Open reviewer authoring post-publication reviews, and a writer committed to science communication and personal essay writing, aiming to produce short course books tied mostly to mathematical biology, publish essays, and grow further as a writer.
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