Youcef Mammeri

Mathematical Modelling
Biomathematics

Upon the conclusion of this LU the student should:
 
- know the aims and philosophical foundations of modelling in applied sciences, and understand its limitations and usage;
- be able to formulate, nondimensionalise, and study both analytically and by using computer-based tools, models from different biological contexts (ecology, evolution, physiology, biochemistry) using the frameworks of deterministic and stochastic differential, difference , and delay differential equations as appropriate.
 

1) Biological background: kinetics of enzymatic reactions, mathematical ecology, some notions of cell and molecular biology;
2) Modelling using Ordinary Differential Equations in biochemical kinetics; Quasi-steady state assumption and its validity;
3) Dealing with stochasticity: Gillespie's algorithm;
4) Modelling in physiology using delay-differential equations;
5) Modelling in mathematical ecology in discrete time: structured populations and methods of linear algebra;
6) Modelling evolution.
 

• Cushing: An Introduction to Structured Population Dynamics, Society for Industrial and Applied Mathematics, 1998
• Erneux: Applied Delay Differential Equations, Springer, 2008
• Murray: Mathematical Biology, 2nd ed. Vols. 1 & 2, Springer, 1993
 

E-learning

Evaluation is made on individual basis and it involves the coexistence of two modes: continuous assessment (60%) and final evaluation (40%). Further information is detailed in the Learning Agreement of the course unit.

This Learning Unit will be taught in English.