UE Mathematical modelling in life science : reaction-dispersion models

Degrees incorporating this pedagocial element :


The course aim to study qualitative and quantitative properties of reaction-dispersion models based on partial differential equations in order to answer modern issues in spatial ecology and population genetics. On the one hand, the course will give opportunity to student to enhance their knowledge in dynamical system and qualitative study of Partial Differential Equation (maximum principles, principal eigenvalues, traveling waves). On the other hand, The course will guide student to open their mind to ecological issue and provide them mathematical tools to achieve this goal.

The course will first introduce in a constructive way, the main interesting and useful models based on partial differential equations that arise in mathematical ecology. Secondly, we will concentrate on the mathematical properties of the these models. More precisely, we will describe mathematical properties of dispersal operators such that the diffusion operator or the convolution operator. Then we will concentrate on the intertwined effect of dispersal and growth. We The course is organized as follows :

  • Non–spatial models (system of ordinary differential equations)
  • Dispersion models (diffusion equations and integro-differential equations)
  • Dispersion and growth models (reaction–dispersion models)
  • Spatio–temporal dynamics of neutral genetic fractions