This biannual learning unit is not being organized in 2020-2021 !
At the end of this learning unit, the student is able to :
Contribution of the course to the program objectives
At the end of the course LMAPR2510, students will be able to:
- Single-species population models: logistic growth model - microbial growth models - age distribution models.
- Populations interactions and biodiversity models: predator-prey Lotka-Volterra models - competitive exclusion principle - coexistence.
- Key elements of mathematical modeling in epidemiology of infectious diseases: compartmental models - dynamics at the population level (epidemics, endemic states) - basic reproduction ratio (R0) - infectious disease control.
- Random walks, diffusion and characteristic time scales.
- Population dynamics in space : advection-diffusion-reaction equations - dynamics of a species in the presence of dispersion - dynamics of several species with dispersion - nonlinear progressive waves - effect of dispersion on populations in competition ' pattern formation.
Due to the COVID-19 crisis, the information in this section is particularly likely to change.The course is taught through lectures that include many examples. Practicals and larger-scale individual projects are also proposed to the students so that they can implement the theoretical concepts covered in the lectures.
Due to the COVID-19 crisis, the information in this section is particularly likely to change.Individual report based on a project and oral defense during the exam session.
This course requires prior training in ordinary and partial differential equations (ODEs and PDEs).
- Supports de cours : Notes de cours et programmes Matlab disponibles sur iCampus.
- Ouvrages de référence : May R.M., 1973, Stability and Complexity in Model Ecosystems, Princeton University Press - Murray J.D., 2002 (3rd ed.), Mathematical Biology (Vol. I & II), Springer - Okubo A., 1980, Diffusion and Ecological Problems: Mathematical Models, Springer-Verlag - Keeling M.J. & Rohani P., 2007, Modeling Infectious Diseases in Humans and Animals, Princeton University Press - Brauer F., van den Driessche P. & Wu J., 2008, Mathematical Epidemiology, Springer.