23313a
Vorlesung
V Introduction to Mathematical Modelling in Biology
Thibault Moulin, Britta Tietjen
Hinweise für Studierende
Additional information on the course: < Modulbeschreibung der Modulvariante Einführung in die Mathematische Modellierung in der Biologie Schließen
Zusätzl. Angaben / Voraussetzungen
Bitte am Rechner arbeiten, auf einem Tablet lässt sich R schlecht installieren!
Kommentar
Lecture:
The lectures will deliver an introduction to the theory of Biological and Ecological modelling, and give insights on how applying those tools to specific ecosystems. The lecture will introduce different topics of mathematical modelling, expose the basic theory of the differential equations systems and its application to describe the time dynamics of biological and ecological systems. Knowledges of differential systems are usefull, as the basis of process-based models widely used in ecology. The purposes of this course are (1) to give an overview of the theory of the differential systems, (2) applying this theory in the particular context of population dynamics in order to describe with models various classical situations emerging in biology and in ecology (prey-predator, consumer-resources, epidemiology), (3) analyze the model, with both analytical and numerical methods, to understand the key behavior of the systems and thus the overall dynamics affecting each populations, (4) understand the key role of functional responses in the writing of models on each populations dynamics behavior, (5) opening to more complex process-based models in the field of community ecology, (6) explore specific technics to understand the behaviour of more complex system (sensitiviy analysis by example). Objectives of this course include:
The lectures will deliver an introduction to the theory of Biological and Ecological modelling, and give insights on how applying those tools to specific ecosystems. The lecture will introduce different topics of mathematical modelling, expose the basic theory of the differential equations systems and its application to describe the time dynamics of biological and ecological systems. Knowledges of differential systems are usefull, as the basis of process-based models widely used in ecology. The purposes of this course are (1) to give an overview of the theory of the differential systems, (2) applying this theory in the particular context of population dynamics in order to describe with models various classical situations emerging in biology and in ecology (prey-predator, consumer-resources, epidemiology), (3) analyze the model, with both analytical and numerical methods, to understand the key behavior of the systems and thus the overall dynamics affecting each populations, (4) understand the key role of functional responses in the writing of models on each populations dynamics behavior, (5) opening to more complex process-based models in the field of community ecology, (6) explore specific technics to understand the behaviour of more complex system (sensitiviy analysis by example). Objectives of this course include:
- Reminder of basic mathematical tools (analysis) to understand the theory of differential equations
- Syntax in R, language that will be used for numerical simulation of the model
- Translating scientific problems into models and the key role of functional responses
- Analytical resolutions of differential equations: steady states of the system, stability and attractivity of the steady states, bifurcation between steady states.
- Numerical resolutions of differential equations, utilization of the DeSolve package, numerical illustration of the analytical results
- Building of a process-based model, based on the theory of this course, make the implementation with R to solve the model and analysis of the key behaviour.