Structured equations in biology

Delphine Salort

Ce cours sera disponible en télé-enseignement et l’évaluation se fera par contrôle réparti (devoir personnels et partiel, pas d’examen final).

Topics :

Since the celebrated Kermack-McKendrick model for epidemiology and the age structured equation , numerous strucured equations have been introduced in order to describe various phenomenon as size distribution, cell receptor repartition, neuron voltage and conductances… One can consider physiological parameters (that change along the organism life) or phrnotypican (inherited at birth). To study such models requires specific tools that we are going to present

• eigen-elements and the Krein-Rutman theorem
• generalized relative entropy
• asymptotic methods
• the Doeblin method

Through some examples, which we will try to relate to other courses of mathematics for biology, we will also treat

• Structured in mathematical epidemiology
• discretisation et and numerical methods
• singular perturbation and singular problems

References :

[1] Benoit Perthame. Transport equations in biology. Birkhauser (2007).

[2] Keener, J. and Sneyd, J. Mathematical physiology. Interdisciplinary Applied Mathematics, 8. Springer-Verlag, New York, 1998.

[3] Edelstein-Keshet, L. Mathematical models in biology, 2nd edition. (2005).

[4] Cushing, J.M. An Introduction to Structured Population Dynamics. CBMS- NSF, Regional conference series in applied mathematics, SIAM (1998).