5.00 credits
30.0 h + 22.5 h
Q2
This biannual learning unit is being organized in 20232024
Teacher(s)
Language
English
> Frenchfriendly
> Frenchfriendly
Prerequisites
This course requires prior training in ordinary and partial differential equations (ODEs and PDEs).
Main themes
This course covers the mathematical modelling of ecological and epidemiological processes in the context of systems theory. It aims to analyse the properties of key ecological and epidemiological models, particularly population models. Basically, the models studied refer to the laws of physics, and in particular the concepts of conservation of matter. This course aims to introduce basic tools for understanding and, if possible predicting, the spatiotemporal evolution of ecological and epidemiological systems. These tools include ordinary differential equations, partial differential equations and numerical methods to approximate these equations.
Learning outcomes
At the end of this learning unit, the student is able to :  
1 
Contribution of the course to the program objectives
At the end of the course LMAPR2510, students will be able to:

Content
The course covers the following elements, in particular through a detailed presentation of examples made using Matlab and/or Python:
 Singlespecies population models: logistic growth model  microbial growth models  age distribution models.
 Populations interactions and biodiversity models: predatorprey LotkaVolterra 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 : advectiondiffusionreaction 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.
Teaching methods
The course is taught through lectures that include many examples. Practicals and largerscale individual projects are also proposed to the students so that they can implement the theoretical concepts covered in the lectures.
Evaluation methods
Individual report based on a project and oral defense during the exam session.
Other information
The notes are written in English. Lectures are given in English.
This course requires prior training in ordinary and partial differential equations (ODEs and PDEs).
This course requires prior training in ordinary and partial differential equations (ODEs and PDEs).
Online resources
Lecture notes and Matlab/Python scripts available on Moodle :
https://moodleucl.uclouvain.be/course/view.php?id=9201
https://moodleucl.uclouvain.be/course/view.php?id=9201
Bibliography
 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, SpringerVerlag  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.
Faculty or entity
Programmes / formations proposant cette unité d'enseignement (UE)
Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Master [120] in Environmental Science and Management
Interdisciplinary Advanced Master in Science and Management of the Environment and Sustainable Development
Master [120] in Electromechanical Engineering
Master [120] in Mathematical Engineering
Master [120] in Physics
Master [120] in Energy Engineering