April 25-26, 2018, University of Waterloo

AN INTRODUCTION TO MATHEMATICAL MODELLING

(QUANTITATIVE METHODS)

April 26, 2018 (9:30-11:30 a.m.)

Lyle Hallman Institute, University of Waterloo

(QUANTITATIVE METHODS)

April 26, 2018 (9:30-11:30 a.m.)

Lyle Hallman Institute, University of Waterloo

**WORKSHOP DESCRIPTION**

Mathematical modelling is becoming increasingly important to the analysis of complex adaptive systems, with applications in ecology, sustainability management, economics, and physics. Both macroscopic and microscopic approaches can be used, depending on the structure and scale of the system being modelled.

The first half of this workshop will be concerned with dynamical systems - a popular framework used to capture interactions between variables on a global scale. We will introduce the concept of a dynamical system, with simple examples for illustration. We will also go through the construction of a model, such as variable selection, interaction types and time scales. This will allow us to brainstorm, and construct a model for an environmental system. Finally, we will discuss parameter fitting and limitations of dynamical systems.

In the second half, we will discuss the use of agent-based models (ABMs), which include spatial structure and stochasticity, unlike dynamical systems modelling. This allows us to explore the complex self-organisation and critical phenomena that can arise from simple rules of local interaction of discrete entities (such as molecules or people). Together, we’ll look at examples of ABMs, as well as model construction, parametrisation, and validation.

This workshop will encourage the use of mathematical modelling in environmental and heath studies, and promote new ideas and perspectives that can be incorporated into current research in complex adaptive systems.

**LEARNING OBJECTIVES**

- Understand the principles of setting up and parametrising a dynamical system
- Construct a simple ABM, choose parameters and rules of interaction of agents
- Understand the relative merits of each approach, and when each is appropriate

**WORKSHOP MATERIALS**

Slides - An introduction to mathematical modelling (PDF)

Worksheet (PDF)

Slides - Agent-based modelling (PDF)

Handout (PDF)

**FACILITATORS**

Thomas Bury: Thomas is a PhD candidate in the Department of Applied Mathematics, under the supervision of Prof. Chris Bauch and Prof. Madhur Anand. Previously, he completed his Masters and undergraduate studies at the University of Cambridge, where he specialised in mathematical applications to biological and theoretical physics. Thomas’ current research concerns the mathematics surrounding regime shifts in complex systems. He is working with epidemiological, ecological and climate models, to better understand how researchers can exploit time-series data to warn of imminent regime shifts.

Brendon Phillips: Brendon is a Ph.D. student at the University of Waterloo, under the supervision of Professor Chris Bauch. His research centres around finding early warning signals of epidemics in large populations.