Stochastic epidemic models

MATH-560 / 5 credits

Teacher:

Language: English

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

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

 

Ressources en bibliothèque

In the programs

  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Stochastic epidemic models
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Stochastic epidemic models
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Stochastic epidemic models
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Stochastic epidemic models
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional

Reference week

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