This module provides a practical introduction to the mathematical modelling of infectious diseases. Mathematical modelling is being used with increasing frequency and scope to address questions about infectious diseases both in terms of basic science and in terms of national and international policymaking. Mathematical modellers arrive at the discipline from many backgrounds ranging from epidemiology to economics. Mathematical modelling is an interdisciplinary activity which brings together elements from mathematics, computer science, economics, demographics, virology, and immunology.
In this module, the students will be supported to develop a set of basic mathematical modelling skills though a mix of practical sessions interspersed with short theory sessions. They will be given a thorough introduction to the core concepts and techniques that will permeate sessions throughout the week and some elective modules. This foundation will be solidified through key working examples and put into practice in R. Throughout the week we will guide the students through the process of building a model suited to address a research/policy question, developing and implementing the model in mathematical and code forms, and interpret the short- and long-term dynamics produced. Starting from simple compartmental models, students will be exposed to a repository of different model typologies that could be used as a template for any future modelling exercise.
Learning outcomes:
By the end of the module, students will be able to:
- Write a simple mathematical model that is appropriate for a specific infectious disease and related research/policy question.
- Understand how critical transmission related parameters, like the reproduction number, affect infectious disease dynamics.
- Critically examine the short- and long-term dynamics of a model.
- Compare and contrast different model outputs to evaluate the effectiveness of different public health interventions.
- Understand the limits of compartmental model in addressing sources of heterogeneity and how to best address them.
- Critically appraise modelling papers.
| Session | Title | Lecturer |
|---|---|---|
| 1 | Introduction to Mathematical Modelling - Concepts and Techniques | Ricardo Águas |
| 2 | Model Structure and Dynamic Implications of Model Structures | Ricardo Águas |
| 3 | Adapting Models - Accounting for Added Complexity or Real Time Incoming Knowledge | Ricardo Águas |
| 4 | Modelling Interventions | Ricardo Águas |
| 5 | Relaxing Model Assumptions - Implementing Heterogeneities | Ricardo Águas |
| 6 | Spatial Models | Ricardo Águas |
| 7 | Age-dependent Models | Ricardo Águas |
| 8 | Modelling for Policy | Ricardo Águas |
| 9 | Individual-based Models | Ricardo Águas |
| 10 | Multi-strain Models | Ricardo Águas |