Institut für Mathematik


Modul:   MAT971  Seminar über stochastische Prozesse

Local weak convergence for a general stochastic SIR model

Vortrag von Dr. Jean-Jil Duchamps

Sprecher eingeladen von: Prof. Dr. Jean Bertoin

Datum: 20.03.24  Zeit: 17.15 - 18.45  Raum: ETH HG G 43

We study an epidemiological model where infections arise in a population according to a general, non-Markovian SIR-like model with a time-dependent contact rate. We make few assumptions, only requiring that the number of potential infections generated by an individual has finite expectation on bounded time intervals. This model can be viewed as a general Crump-Mode-Jagers model with interactions, and we study the local weak convergence of its infection graph, which yields (1) a functional law of large numbers for our SIR process, and (2) the identification of a "contact-tracing Markov process" that traces back the chain of infection leading to a typical individual. This is joint work with Félix Foutel-Rodier and Emmanuel Schertzer.