Mathematical Epidemiology of Infectious Diseases
Important : Please check https://indico.math.cnrs.fr/event/5810/ for the exact dates and locations of this course.
The course will concentrate on
- the formulation of mathematical models of the spread of an infectious disease in a host population;
- the analysis of such models;
- the derivation of epidemiological insights by interpretation of the results of the analysis.
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
- 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 !)
- Heterogeneity : the next-generation matrix/operator, the basic reproduction number (Perron- Frobenius, Krein-Rutman), the Malthusian parameter and the nal size equation
- Compartmental models
- Including demographic turnover : age structure
- Spatial Spread
- Waning Immunity
- 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