Mathematical biology is an active and fast-growing interdisciplinary field in which mathematical concepts, techniques, and models are applied to problems in biology and medicine. Many biological processes can be described by differential equations and difference equations. This course introduces students to the construction and analysis of these models. We will cover a wide variety of topics including single-species models, nonlinear dynamics and chaos, (predator-prey and competition) models for interacting populations, enzyme kinetics, biological oscillators, neural and physiological models (excitability, testoserone secretion), pharmacokinetics, and models from epidemiology.

• Continuous-time population dynamics
• Population models with age structure
• Discrete-time population dynamics
• Tumour growth and cell proliferation
• Continuous-time interacting population models
• Discrete-time models for interacting populations
• Enzyme kinetics
• Simple oscillatory reactions
• Hodgkin-Huxley theory and neural networks
• Belousov-Zhabotinskii reaction
• Coupled oscillators
• Epidemiology models and dynamic diseases
• Pharmacokinetics and drug action
• Blood flow and dynamics