3MC Math Epi course organisation

4 April 2022

Julien Arino

Department of Mathematics & Data Science Nexus
University of Manitoba*

Canadian Centre for Disease Modelling
Canadian COVID-19 Mathematical Modelling Task Force
NSERC-PHAC EID Modelling Consortium (CANMOD, MfPH, OMNI/RÉUNIS)

* The University of Manitoba campuses are located on original lands of Anishinaabeg, Cree, Oji-Cree, Dakota and Dene peoples, and on the homeland of the Métis Nation.

In Memoriam - Fred Brauer

Fred Brauer was a friend and mentor to many worldwide and an éminence grise of Mathematical Epidemiology in Canada

I was privileged to learn from him and teach math epi with him in a wide variety of settings

Fred passed away 2021-10-17. This course is dedicated to his memory!

When you learn to use a hammer, everything looks like a nail

About the course

Getting in touch

  • Just email me (email is on the title page)
  • Do add something like [3MC] in your subject line, I get (too) many emails

GitHub repository for the course

Most course material is available from a GitHub repository/page I set up:
https://julien-arino.github.io/3MC-course-epidemiological-modelling

This includes the slides, code and data samples

This does not include bibliographic references, although there are links to articles and books. As much as possible, I link to Open Access sources

One remark: I sometimes refer to Wikipedia. For the younger students here: this can be where you first look, not what you cite in proper work

Slides

  • Slides are written in Markdown and LaTeX and are rendered as html files using Marp running in the Visual Studio Code editor

  • Image files are mostly not hosted locally and thus require internet access

  • As much as possible, I have indicated provenance (by linking the file on the original website); when not possible, the file is saved with the name of the source indicated

  • Figure sources are added as html comments which appear as "speakers notes" in the presentation version

Videos

  • Videos are being recorded for the course
  • They are posted on YouTube
  • You can access the playlist here. Links to individual videos are also available on the webpage

Code

  • I use R - Python would be a good choice as well but I prefer R
  • Instructions on setting up R for the course can be found in the GitHub repo
  • Some code is in the repo
  • For the epi side of things, a very useful open reference: R for applied epidemiology and public health

Reading recommendations (math epi)

The following are my favourite references:

Course objectives

Introduction to Mathematical Epidemiology

  • Problems
  • Methods

We will have these particular problems in mind:

  1. Modelling techniques
  2. Mathematical analysis of models
  3. Computational analysis of models
  4. Use of data

It is important to do the 4 interactively

About modelling

  • Do not neglect this step
  • Think outside the box
  • Take the time
  • Try to remain simple

About mathematical analysis

  • Used to be the sole purpose of most papers
  • Judge your audience: global stability is cool, but is it really required if you want to present work to a public health person?
  • Do as much as possible (for instance, knowing the value of can be useful to set parameters), do not hesitate to move to an appendix

About numerics

  • Numerics should be used to complement the mathematical analysis

  • If you have shown the global stability of some equilibrium point, no need to show a simulation where solutions converge to this equilibrium

  • In fact, it is rarely useful to show a solution (cases where it is okay: before going to zero the number of infectious does something really cool, you have a period doubling, etc.)

  • Instead, use numerics to investigate scenarios or test the effect of varying parameters

  • A good figure tells a story, it is worth spending time thinking about how to make good figures

About data

  • Acquiring data has become much easier than even 20 years ago
  • As a modeller, it is not necessary that everything be data-driven, but it is necessary to be "context-aware" (this means getting a sense of the quantities involved in the process you want to model)

Organisation of the course

L1: History of epidemics and Historical epidemics
L2: Basic concepts of Mathematical Epidemiology. Models in one population
P1: Introduction to R. Collecting data. Solving ODEs in R
L3: Epidemics spreading among groups. Epidemics spreading in space and time
L4: Group models
L5: Metapopulation models
P2: Model analysis, studying large-scale models in R
L6: Stochastic aspects in the spread of epidemics
L7: Stochastic epidemic models
L8: Agent-based models
P3: Analysis, studying stochastic models in R. Simulating agent-based models
L9: Some recent mathematical models for COVID-19, HIV/AIDS, TB, Malaria, etc.

Colour codes for course organisation