Sorbonne Université

Master de Sciences & Technologies

M2 Mathématiques & Applications (Sorbonne Université)

Mathematical Epidemiology of Infectious Diseases

Luis Almeida Sorbonne University and Odo Diekmann Utrecht University

Important : Please check for the exact dates and locations of this course.

Topics :

The course will concentrate on

The course focusses on deterministic population level models, but with due attention for the underlying stochastic processes at the individual level. From a mathematical point of view, the emphasis is on Renewal Equations, a certain kind of delay equations. There will be some, but not much, attention for data analysis and control efforts.

A preliminary list of topics is

  1. Epidemic outbreak in a demographically closed population (or: what is the celebrated 1927 paper of Kermack & McKendrick all about ? Not (just) about the SIR and SEIR compartmental models !)
  2. Heterogeneity : the next-generation matrix/operator, the basic reproduction number (Perron- Frobenius, Krein-Rutman), the Malthusian parameter and the nal size equation
  3. Compartmental models
  4. Including demographic turnover : age structure
  5. Spatial Spread
  6. Waning Immunity
  7. Dangerous Connections: on binding sites models

Literature :

O. Diekmann, J.A.P. Heesterbeek, T. Britton, Mathematical Tools for Understanding Infectious Disease Dynamics, Princeton University Press, 2013