Stochastic Epidemic Models
Summer semester 2020
The current outbreak of Covid 19 is a thread to people worldwide. It also raises interest in epidmiology - a branch of science that deals with the incidence, distribution, and control of disease in a population.
This seminar deals with the mathematical foundations of epidemiology. You will not learn anything specific about the Covid-19 outbreak, neither about the Corona virus. However, you will learn how such an outbreak can be modelled as a random process, and how probability theory can be used to understand such outbreaks.
Target group: Master students in Mathematics, TMP, Finance- and Insurancemathematics
Bachelor students with strong background in Probability Theory and keen interest in the topic may apply for admission.
Prerequisites: Solid foundations in probability theory
Lecturer: Markus Heydenreich
Registration: Please sign up for the seminar at Uni2Work.
Time: Fridays 8:30-10:00. We start online, and shall return to conventional meetings if the situation allows.
ResourcesOur main text is the textbook Stochastic Epidemic Models and their Statistical Analysis by Håkan Andersson and Tom Britton (Springer 2000), available through our university library or as free preprint on the author's home author's homepage.
Futher material: Two papers by Frank G. Ball, David J. Sirl, and Pieter Trapman, Threshold behaviour and final outcome of an epidemic on a random network with household structure and Epidemics on random intersection graphs. Further a paper by Svante Janson, Malwina Luzcak and Peter Windridge, Law of large numbers for the SIR epidemic on a random graph with given degrees
||SIR epidemics (Chapter 2)||A.G.|
||Coupling methods (Chapter 3)||L.B.|
||Threshold limit theorems (Chapter 4)||S.C.|
||Density dependent jump Markov processes (Chapter 5)||S.C.|
||Multitype epidemics (Chapter 6)||J.B.|
||--- (bridge day)|
||Epidemics and graphs (Chapter 7)||C.R.|
||LLN for epidmics on graphs with given degrees (Jan-Luc-Win paper)||R.S.|
||Statistics for epidemic processes (Chapter 9)||U.Ö.|
||Estimation in partially observed epidemics (Chapter 10)||S.R.|
||MCMC methods (Chapter 11)||J.B.|
||Vaccination (Chapter 12)||E.S.-F.|
The meetings start at 8:30 via Zoom. The link has been communicated (and is avaiblable on uni2work).