Advanced studies in Theoretical and Computational Biology

Jan 6, 2025 — Apr 8, 2025

About the course

The purpose of this graduate course is to equip graduate students with cutting-edge techniques in data-driven mathematical and computational modelling, analysis and simulations of semi-linear parabolic partial differential equations (PDEs) of reaction-diffusion type. It will cover diverse areas in data-driven modelling using PDEs in biology. I will cover approaches on formulating models from data using first principles, mathematical analysis of reaction-diffusion systems such as linear stability analysis, basic concepts on bifurcation analysis and numerical bifurcation analysis. The second part will focus on numerical methods for PDEs including finite difference methods, and finite elements. This part will also deal with time-stepping schemes and nonlinear solvers for nonlinear PDEs. If time allows, we will look at applications of reaction diffusion theory to cell motility and pattern formation. To support theoretical modelling and numerical analysis, numerical algorithms will be developed and implemented in MATLAB as well as in open finite element source software packages such as FeNiCs, deal.ii and others. Students will be allowed to use packages of their choice as appropriate. Expertise and skills sets to be acquired through this course

1. Acquire data-driven modelling skills and techniques in PDEs and their applications to biology
2. Acquire techniques and knowledge in mathematical analysis of reaction-diffusion systems
3. Acquire expertise and skills in bifurcation analysis, numerical bifurcation, and sensitivity analysis
4. Acquire numerical analysis techniques and skills to compute approximate numerical solutions
5. Acquire expertise and knowledge in finite difference methods for semi-linear parabolic PDEs
6. Acquire expertise and knowledge in finite element methods for semi-linear parabolic PDEs
7. Gain some knowledge in bulk-surface PDEs, and their analysis (might be covered if time allows) Key

Registration

This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

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