# Mathematical Modelling of Infectious Diseases

#### Lecturers

Associate Professor Roslyn Hickson, CSIRO and James Cook University

#### Synopsis

Infectious disease transmission is a nonlinear process with many subtleties and complications more sociological in nature (e.g. how people behave). Mathematical modelling of infectious disease transmission has substantial potential real world application, as highlighted by the recent COVID-19 pandemic.

This course explores key topics in infectious disease modelling, including the development of appropriate models, parameterisation from data using Bayesian Inference, and using models as a “what-if” scenario tool or as a tool to increase understanding of fundamental epidemiological processes. We will start with quite simple mathematical models that yield important insights to disease dynamics and control, and build to more complex models that better reflect complicated infectious disease dynamics. The focus will be on simulation of these models, as opposed to analytical analysis.

#### Course Overview

• What is modelling? Introduction to epidemiology
• Compartmental modelling
• Parameterisation of models: What to do with data?
• Controlling infectious diseases, including a case study
• Spatial models
• Introduction to agent-based approaches

#### Prerequisites

• Systems of differential equations
• Need to be able to solve dP/dt = b P(t)
• Understanding how to get from a problem description to a differential equation
• Understanding stability of equilibria will be helpful.
• Basic probability
• Understanding Bayes’ theorem/rule is an advantage.
• Programming (at least basic)
• Python will be used extensively throughout the course, so familiarity with the basics of Python will be advantageous.
• No prior biological or epidemiological knowledge is expected.

#### Assessment

• Assignment (20%)
• Computer lab worksheets (20% in total)
• Short online quizzes following lectures (20% in total)
• Final project assignment (40% total), composed of:
• 2 page checkpoint summary and proposal plan due in the last week of Summer School (10/40)
• Final report (and code) due during Summer School exam period (30/40)

Lecture notes will be provided during the course that complement the following book by Keeling and Rohani

• We will work a lot from Modelling Infectious Diseases: In animals and humans, by Keeling and Rohani. They also have a website with example code.
• Optionally: The Handbook of Infectious Disease Data Analysis, by By Leonhard Held, Niel Hens, Philip D O’Neill, Jacco Wallinga.