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* Corresponding author 1 LPTM - Laboratoire de Physique Théorique et Modélisation

Abstract : We study the impact on shape parameters of an underlying Bienaymé-Galton-Watson branching process height, width and first hitting time, of having a non-spatial branching mechanism with infinite variance. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion BBM we then consider spatial branching processes in dimension d, not necessarily integer. The underlying branching mechanism is then either a binary branching model or one presenting infinite variance. In particular we evaluate the chance px of being hit if the epidemics started away at distance x. We compute the large x tail probabilities of this event, both when the branching mechanism is regular and when it exhibits very large fluctuations.

Keywords : evolutionary genetics and epidemics Bienaymé-Galton-Watson process branching Bessel process extreme events. extreme events





Autor: Jean Avan - Nicolas Grosjean - Thierry Huillet -

Fuente: https://hal.archives-ouvertes.fr/



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