An overview of Modelling Infectious disease by Iain Moyles (Math & Stats, York U), Bouchra Nasri (École de Santé Publique, Université de Montréal) and Idriss Sekkak (École de Santé Publique, Université de Montréal)

This 6-hour course aims to give an overview about infectious disease modeling. The workshop will begin with the concepts mathematical modelling and how they can be used to model disease outbreaks. It will explore different model structures including compartmental and stochastic models and how modelling provides a deeper understanding of disease dynamics. Finally, we focus on the selection and use of models as predictive tools and to better understand fundamental epidemiological processes. This course offers a step-by-step introduction to infectious disease modeling, from basic concepts to the appropriate choice of models.

The outline of the course is detailed below:
 
Part 1: Introduction: Philosophy of modelling, the basic elements of infection and transmission, Definitions, types, and characterization of infectious diseases. Epidemiological models.  Notions of differential equations and the differential equation limit of a model.

Part 2: Compartmental Models: Compartment-based epidemiological models. The basic epidemiological model SIR (Susceptible-Infected-Recovered) and related concepts, including the calculation of R0, the equilibrium point, and final size.  Analysis of host strategies and heterogeneities (compartments by age, by risk, etc.). Transition to PDE.
 
Part 3: Stochastic Models: Stochastic epidemiological models. Stochastic compartment models: Motivation and concepts. Mathematical analysis and numerical approximations of stochastic epidemiological models.

Part 4: Model Determination: Selecting an appropriate model for an infectious disease. The different types of compartment models.  Modeling immunity and incubation time. Selection of model structure.
 
This 6-hour course is based on lectures with exercises based on case studies in infectious disease epidemiology. R codes for basic models and structural modifications.