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On the outcome of epidemics with detections

  • Claude Lefèvre (a1) and Philippe Picard (a2)


The classical SIR epidemic model is generalized to incorporate a detection process of infectives in the course of time. Our purpose is to determine the exact distribution of the population state at the first detection instant and the following ones. An extension is also discussed that allows the parameters to change with the number of detected cases. The followed approach relies on simple martingale arguments and uses a special family of Abel–Gontcharoff polynomials.


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* Postal address: Département de Mathématique, Campus de la Plaine C.P. 210, B-1050 Bruxelles, Belgium. Email address:
** Postal address: Ecole ISFA, 50 Avenue Tony Garnier, F-69007 Lyon, France. Email address:


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