Mathematical Biology
Chemistry & Life Sciences
Mathematical modeling of biological systems: population dynamics, epidemiology, reaction-diffusion, evolutionary dynamics, and neuroscience.
Learning Objectives
- Analyse predator-prey and competition dynamics with Lotka-Volterra equations
- Compute the basic reproduction number and herd-immunity threshold for epidemic models
- Derive and apply the Michaelis-Menten rate law using the quasi-steady-state approximation
- Identify conditions for Turing instability in reaction-diffusion systems
- Use the replicator equation and Price equation in evolutionary dynamics models
- Simulate exact stochastic trajectories with the Gillespie algorithm
- Explain the Hodgkin-Huxley model of the neuronal action potential
Lessons
1
Population Dynamics: Lotka-Volterra & Competition
35 min
2
Epidemiology: SIR & SIS Models
35 min
3
Reaction Kinetics & Michaelis-Menten
35 min
4
Reaction-Diffusion & Pattern Formation (Turing)
35 min
5
Evolutionary Dynamics & Fitness Landscapes
35 min
6
Stochastic Biology: Master Equation & Gillespie
35 min
7
Computational Neuroscience: Hodgkin-Huxley
35 min
Quick Practice
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Key Concept Flashcards
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