Stochastic epidemic models
Summary
This course is an introduction to some classical models of epidemics involving random mechanisms.
Content
- Basics on Branching processes and Poisson process
- Stochastic compartment model: basic reproduction number, probability of a major outbreak, final size of the epidemic, vaccination
- Markovian compartment models: functional law of large numbers and central limit theorem, diffusion approximation
- (Non-markovian) closed models: final size of the epidemic, duration of the epidemic
- Epidemic models with two levels of mixing: probability of a major outbreak, final size of the epidemic
Keywords
Stochastic epidemic, basic reproduction number, branching processes, limit theorems
Learning Prerequisites
Required courses
MATH-330 : Martingales et mouvement Brownien
MATH-332 : Stochastic processes
MATH-432 : Probability theory
Important concepts to start the course
Students are expected to be familiar – at least able to catch up quickly – with (discrete) martingales, Markov chains and convergence of random variables. Recalls will be made during the first lectures and exercise sessions.
Teaching methods
Lectures followed by exercise sessions
Assessment methods
Written
Resources
Bibliography
Stochastic Epidemic Models with Inference – Tom Britton and Etienne Pardoux
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Ressources en bibliothèque
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Stochastic epidemic models
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Stochastic epidemic models
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Stochastic epidemic models
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Stochastic epidemic models
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
Semaine de référence
| Lu | Ma | Me | Je | Ve | |
| 8-9 | |||||
| 9-10 | |||||
| 10-11 | |||||
| 11-12 | |||||
| 12-13 | |||||
| 13-14 | |||||
| 14-15 | |||||
| 15-16 | |||||
| 16-17 | |||||
| 17-18 | |||||
| 18-19 | |||||
| 19-20 | |||||
| 20-21 | |||||
| 21-22 |
Légendes:
Cours
Exercice, TP
Projet, autre