Course: Mathematical Epidemiology of Infectious Diseases (O. Diekmann, L. Almeida), on Mondays 10h-12h

17 janv. 2022, 10:00 → 26 mars 2022, 12:00 Europe/Paris

This will be a blackboard course. 

If you have questions about this course, please send a mail to

O.Diekmann @t uu.nl   and luis.almeida @t sorbonne-universite.fr

Topics :

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

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 final 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

 

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20220117NotesDiekman.pdf

20220124NotesDiekman.pdf

20220131NotesDiekman.pdf

20220207NotesDiekman.pdf

20220214NotesDiekman.pdf

20220228et0307NotesDiekman.pdf

20220314NotesDiekman.pdf

20220321NotesDiekman.pdf

Course Abstrat : Mathematical Epidemiology of Infectious Diseases

Topics :

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

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