Université catholique de Louvain - Mathematical ecology - en-cours-2021-linma2510
UCLouvain - en-cours-2021-linma2510 - page 1/3
linma2510
2021 Mathematical ecology
5.00 credits 30.0 h + 22.5 h Q2
This biannual learning is being organized in 2021-2022
Teacher(s) Deleersnijder Eric ;Hanert Emmanuel ;Van Effelterre Thierry ;
Language : English
Place of the course Louvain-la-Neuve
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 spatio-temporal evolution of ecological and epidemiological systems. These tools include ordinary differential
equations, partial differential equations and numerical methods to approximate these equations.
Learning outcomes
1
Contribution of the course to the program objectives
•1.1, 1.2, 1.3
•2.2, 2.4
•3.1, 3.2, 3.3
•5.3, 5.5, 5.6
Specific learning outcomes of the course
At the end of the course LMAPR2510, students will be able to:
•Identify, describe and explain the theoretical concepts of mathematical modeling of ecological and
epidemiological processes in the context of systems theory ;
•Explain mathematical concepts and computer tools to model the spatio-temporal dynamics of these
processes ;
•Activate and mobilize these concepts and tools in an operational manner in order to model the
processes governing an ecological or epidemiological application, through an individual project ;
•Justify and defend the methodological choices that were made for the complete analysis of the case
study, integrating into the discussion the underlying theoretical concepts presented in the course and
illustrated in practical work ;
•Write a brief report, argued on the basis of results and appropriately illustrated with graphs and charts,
using accurate and appropriate scientific vocabulary
- - - -
The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s)
can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Evaluation methods 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.
Teaching methods 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.
Content The course covers the following elements, in particular through a detailed presentation of examples made using
Matlab and/or Python:
1. Single-species population models: logistic growth model - microbial growth models - age distribution models.
2. Populations interactions and biodiversity models: predator-prey Lotka-Volterra models - competitive exclusion
principle - coexistence.
3. 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.
4. Random walks, diffusion and characteristic time scales.
5. 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.
Inline resources Lecture notes and Matlab scripts available on Moodle :
https://moodleucl.uclouvain.be/course/view.php?id=9201
