Laboratoire J.-L Lions, UPMC

and INRIA

**Abstract**: Several Integro-Differential equations and Transport
equations are used to describe growth processes in biological or medical
modeling.

**Lecture 1:**- Models of structured populations: cell populations
structured by age, size, molecular content in some protein. The cell division
cycle. An example: a model of neurone network.
**Lecture 2:**- Perron-Froebenius theory, PDEs and and general relative
entropy
**Lecture 3:**- The case of size structured equation;
**Lecture 4:**- Example of cancer: a general introduction; circadian
rhythm, Floquet theory in PDEs. How to compare the growth processes with and
without periodic control. Application to tumor growth and chronotherapy.
**Lecture 5:**- Example of prion aggregates.