Nonlinear Processes in Biology
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Introduction
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Population dynamics
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Continuous models for single species
Malthus model
The Verhulst (logistic) model
Generalizations and modifications of the Verhulst model
Models of interacting populations: prey-predator
The Lotka-Volterra model
More realistic: the May model
Notebooks:
The Lotka-Volterra model with SAGE
Analysis of the May model with SAGE
Plot of stability condition in 3d
Chemical Kinetics
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Introduction to the kinetics of chemical reactions
Autocatalytic reactions
Example 1
Example 2
Enzyme reactions
Theoretical analysis a’la Michaelis-Menten
The quasi-steady state approximation
Rate of the enzymatic reaction
Notebooks:
Modeling tumor cell growth
Reaction diffusion systems
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Reaction-diffusion equations
Example: diffusion
The Malthus model with migration: The Skellam equation
Verhulst model with migration: Fisher-Kolmogorov equation
Analysis of the Fisher-Kolmogorov equation
Numerical analysis of the Fisher-Kolmogorov equation:
Modelling epidemics
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Epidemic model of Kermack-McKendrick
Example of a set of parameters
Example of epidemic
Geographical spread of epidemic
Realistic modeling of spatial epidemic spread
Model of epidemic spread in homogeneous media
Model of epidemic spread in random geometry
Laplace operator with the reflected wall
Nonlinear processes in Biology
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Continuous models for single species
Models of interacting populations: prey-predator
The Lotka-Volterra model with SAGE
Analysis of the May model with SAGE
Plot of stability condition in 3d
Introduction to the kinetics of chemical reactions
Autocatalytic reactions
Enzyme reactions
Theoretical analysis a’la Michaelis-Menten
Modeling tumor cell growth
Reaction-diffusion equations
The Malthus model with migration: The Skellam equation
Verhulst model with migration: Fisher-Kolmogorov equation
Epidemic model of Kermack-McKendrick
Geographical spread of epidemic
Realistic modeling of spatial epidemic spread
Related Topics
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Continuous models for single species
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