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Talk Abstract
Contact Tracing in Stochastic and Deterministic Epidemic Models

Johannes Müller
Auf der Morgenstelle 10, Bau C
University Tübingen
D-72070 Tübingen

Joint work with Mirjam Kretzschmar, Bilthoven (NL) and Klaus Dietz, Tuebingen.

We consider a simple unstructured individual based stochastic epidemic model with contact tracing. Even in the onset of the epidemic, contact tracing implies that infected individuals do not act independently of each other. Nevertheless, it is possible to analyze the embedded non-stationary Galton-Watson process. Based upon this analysis, threshold theorems and also the probability for major outbreaks can be derived. Furthermore, it is possible to obtain a deterministic model that approximates the stochastic process, and in this way, to determine the prevalence of disease in the quasi-stationary state and to investigate the dynamics of the epidemic.

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  1998-1999 Mathematics in Biology