Course Purpose
The overall aim of this course is to introduce students to the core skills in constructing and simulating mathematical system models. Students will build an appreciation for systems-thinking and its role in modelling of systems with complexity through a set of hands-on modelling applications including disease vector modelling, ecosystem modelling, social networks and agent-based modelling.
Course Learning Outcomes
ELO1: Define properties, features, and representations of complex systems with an emphasis on examples.
ELO2: Explain the need for systems thinking when studying complex systems.
ELO3: Analyse the different approaches to systems modeling to develop a qualitative understanding.
Course Content
This introductory module provides a foundation for using mathematical modelling to understand systems. You will revisit key mathematical tools such as differential and difference equations, and learn to interpret equations qualitatively within their context. Emphasis is placed on computer-aided simulation rather than purely analytical solutions.
This module explores the basic question of “What is a model?” and examines broad model categories. You will learn to distinguish between qualitative and quantitative models, static and dynamic models, and analytical versus numerical models.
This topic introduces two fundamental approaches to mathematical modelling: discrete and continuous models. You will compare these approaches and understand when each style is suitable for representing a situation.
This module examines the distinction between empirical (observation-based) and theoretical (mechanistic-based) models, highlighting how each approach informs modelling decisions and interpretations.
This topic explores deterministic models, which produce consistent outputs for a given setup, versus stochastic models, which incorporate randomness. You will investigate how real-world systems may lie between these approaches.
This module introduces top-down (macroscopic) and bottom-up (microscopic) modelling approaches. You will learn how these perspectives influence the representation and understanding of systems.
This topic defines complex systems, their characteristic features, and classification. You will also explore qualitative examples of complexity in real-world systems to build intuition for modelling challenges.
This module examines “wicked” problems and how systems thinking principles can guide the analysis and intervention of complex systems. You will learn approaches to model complexity effectively.
This topic emphasizes making models responsive to external stimuli, allowing them to interact within broader frameworks. You will explore the benefits of open models in capturing system complexity.
This module introduces hybrid models, which combine multiple modelling paradigms, such as differential equations with agent-based models. Modern hybrid models also integrate data-driven machine learning with process-based understanding for advanced system analysis.