MATH-560 / 5 crédits

Enseignant:

Langue: Anglais

Remark: Pas donné en 2024-25

## Summary

This course is an introduction to some classical models of epidemics involving random mechanisms.

## Content

1. Basics on Branching processes and Poisson process
2. Stochastic compartment model: basic reproduction number, probability of a major outbreak, final size of the epidemic, vaccination
3. Markovian compartment models: functional law of large numbers and central limit theorem, diffusion approximation
4. (Non-markovian) closed models: final size of the epidemic, duration of the epidemic
5. 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

## 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 â€“ at least able to catch up quickly â€“ 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

Written

## Bibliography

Stochastic Epidemic Models with Inference â€“ Tom Britton and Etienne Pardoux

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## 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

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