At the end of the course, the student should be able to:
- identify the added value of Complex Systems approach (or “Systems Thinking” as it is often called) in a discipline
- develop an understanding for levels of aggregation, in particular, how Complex Systems concepts like Emergence, Evolution, Adaptation, Transition and Resilience plays out at different scales of aggregation
- build models in the three disciplines that constitute this interdisciplinary course: climate science, biology and epidemiology
- solve problems in these three disciplines and draw meaningful conclusions relevant for these disciplines
The course exists of three modules.
Each module will have its own assessment. They will be combined with equal weights to determine the final grade.
VWO Mathematics level B.
It will be handy if the students have the basic knowledge of
- Differential equation models
- Phase-space analysis
- Linear algebra and matrix operations
- Probability and statistics, and basic programming skills.
This is a course in three equal modules, sequentially: climate science, biology and epidemiology.
Note that this course builds upon the knowledge and competencies gained in courses BETA-B1CS and BETA-B2CSA.
In the first part of the climate module, we will discuss climate variability and change and focus on the issue of tipping behavior. We will then use aspects of complex systems science methods to study and understand several of these tipping phenomena.
The second part is about avoiding dangerous climate change – without disrupting the economy.
Coming up with an optimal climate policy while assuming a single all-powerful global planner is difficult enough, but implementing it in a system of interacting agents – from states to companies and citizens – who all have their own interests, is complex indeed.
Complexity methods such as agent-based modelling and game theory may help to understand these issues.
The module on biology will cover a handful of biological processes and patterns that have been studied with complexity approaches.
We will cover biological evolution in a spatial context, the formation of spatial patterns, and self-learning random immune systems.
Each topic will be introduced in a lecture that will be followed by a hands-on computer practical (using R and Python).
We will read and discuss papers on a subset of the topics covered.
At the end of the module, students have seen a variety of complexity approaches being applied to interesting biological questions. At the exam they will be tested on this combination.
The module on epidemiology will start with simple mathematical models for epidemic dynamics.
We will then proceed to situations, where complex dynamics can arise and will investigate which types of biological processes in the host – pathogen interaction may lead to these dynamics.
We will then move on to models of epidemics on networks.
Finally, we will consider the impact of heterogeneity in the host population and discuss various ways of modelling epidemics in heterogeneous populations, and we will pay attention to fitting models to data.
Exercises will consist of a combination of pen-and-paper exercises and computer practicals. Some papers from the literature will be read and discussed.
Lectures/tutorials with home exercises and projects.
For the climate science and the epidemiology parts readers (parts of books/papers) and lecture slides will be provided.
For the biology part we will use the book “Complexity a guided tour” by Melanie Mitchell.