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The Mathematics of Bacterial Growth in the Chemostat Bioreactor

A Foundation Course in Chemostat Modelling

This book is 100% completeLast updated on 2026-07-09
Abdurrahman Tukur

How chemostat bacterial systems grow, wash out, or stabilize, modeled from first principles through stability analysis and optimal harvest calculus.

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How chemostat bacterial systems grow, wash out, or stabilize, modeled from first principles through stability analysis and optimal harvest calculus.

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MathematicsBiology

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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.

Contents

Table of Contents

  • Preface
  • 1 The Origins of Continuous Culture Theory
    • 1.1 Before the Chemostat: Batch Culture and Its Limitations
    • 1.2 Monod and the Kinetics of Growth
    • 1.3 The Invention of the Chemostat
  • 2 The Physical Setup and the Meaning of the Variables
    • 2.1 The Chemostat as a Physical Device
    • 2.2 Concentrations, Densities, and Total Masses
    • 2.3 The Monod Growth Function in the Model
  • 3 Deriving the Chemostat Model from First Principles
    • 3.1 The Nutrient and Bacterial Balance
    • 3.2 The Complete Chemostat Model
  • 4 Non-Dimensionalising the Chemostat Model
    • 4.1 The Purpose of Nondimensionalisation
    • 4.2 Choosing the Rescaling Variables
    • 4.3 Rescaling the Nutrient and Bacterial Equations
    • 4.4 The Dimensionless System and Its Parameters
  • 5 The Equilibrium Points of the Dimensionless System
    • 5.1 What an Equilibrium Means
    • 5.2 Computing the Washout Equilibrium
    • 5.3 Computing the Coexistence Equilibrium
    • 5.4 Conditions for Biological Validity
  • 6 Stability Analysis of the Dimensionless System
    • 6.1 The Dilution Rate as a Per-Capita Loss Rate
    • 6.2 The Jacobian Matrix of the System
    • 6.3 Local Stability of the Washout Equilibrium
    • 6.4 Local Stability of the Coexistence Equilibrium
    • 6.5 The Conservation Law and Global Stability
    • 6.6 The Complete Stability Picture
  • 7 Optimising the Bacterial Harvest from the Chemostat
    • 7.1 The Harvest Rate and Its Dependence on the Dilution Rate
    • 7.2 Finding the Optimal Dilution Rate
  • 8 Chemostat in the Context of Mathematical Biology
    • 8.1 Structural Analogies with Epidemic Models
    • 8.2 The Chemostat as a Resource-Consumer Prototype
    • 8.3 Directions for Further Study

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