Contents

• Introduction
  • What is this?
  • What mathematics will we use?
  • What applications will we see?
  • Who is this aimed at?
  • How do I use this book?
  • What is an Open Education Resource?
  • Feedback
• Part I. Population ecology
• 1. Single population models
  • A first population model
  • The logistic equation
  • Case study: spruce budworm
• 2. Interacting populations 1: competition
  • Case study: Red and grey squirrels
  • Analysis
  • A bifurcation diagram
• 3. Interacting populations 2: predator-prey
  • A simple predator-prey model
  • A more realistic model
  • Hopf bifurcation
• Part II. Infectious disease
• 4. Epidemics in human populations
  • the Susceptible-Infected-Recovered model
  • Analysis
  • The basic reproductive ratio, $latex R_0$
  • The epidemic curve
• 5. The SIR model with demographics
  • Including Births and Deaths
  • Endemic disease
  • Vaccination
• 6. Diseases of ecological populations
  • Introduction
  • A case study: controlling rabbits in Australia
  • A free-living parasite model
• 7. Evolution and adaptive dynamics
  • Introducing evolution
  • Resident dynamics
  • Fitness
  • The evolution of parasite virulence
• Part III. Immune and cell dynamics
• 8. A within-host Covid-19 model
  • A model for Covid-19
  • A graphical analysis
  • Linear stability analysis
• 9. A within-host HIV-I model
  • Case study: HIV-I
  • A (pre-treatment) model
  • Treatment
• 10. Introducing models of cancer dynamics
  • Introducing cancer models
  • Single variable models
  • Two variable models
  • Summary
• 11. A model of cancer volume dynamics
  • A model for angiogenesis
  • Anaylsis
  • Treatment
• Part IV. Gene networks
• 12. Introducing gene networks
  • A quick guide to cells and genetic networks
  • A first model
  • Constant transcription
  • Oscillating transcription
• 13. Autoregulation 1: auto-repression
  • regulatory feedback loops
  • Constructing the phase portrait
  • Auto-repression: a negative feedback
  • Sketching the phase portrait
• 14. Autoregulation 2: auto-activation
  • Auto-activation: a positive feedback
  • Using phase portraits
  • An example transcription function
• 15. Longer negative feedback networks
  • A simplified 3-variable model
• 16. A two-gene toggle switch
  • A general model form
  • Biological significance
• Part V. Pharmacokinetics
• 17. Single intravenous bolus dose
  • What is pharmacokinetics?
  • A single dose model
  • Drug half-life
• 18. Repeated intravenous bolus doses
  • Why repeated doses might be a problem
  • Mathematical derivation
  • Loading dose and maintenance dose
• 19. Single and repeated oral doses
  • Developing a 2-compartment model
  • Repeated oral doses
  • Example problems
• 20. A two compartment bolus model
  • A bloodstream-tissue model
  • Solving a system of linear equations
• Part VI. Background reviews
• 21. Phase portraits
  • A Graphical analysis
  • Algorithm
• 22. Linear stability analysis
  • Introduction
  • One-Dimensional systems
  • Two-dimensional systems
  • Higher-Dimensional systems
• 23. Bifurcations
  • Introducing bifurcations
  • Standard bifurcations
• Final thoughts and acknowledgements
  • Summary
  • Further study
  • Acknowledgements
  • About the author
• References