arXiv subjects

Ibrahima Drame

Publications and source records attributed to Ibrahima Drame.

4 recordsLinked to original sources

arXiv2023

Extinction time of an epidemic with infection age dependent infectivity

This paper studies the distribution function of the time of extinction of a subcritical epidemic, when a large enough proportion of the population has been immunized and/or the infectivity of the infectious individuals has been reduced, so that the effective reproduction number is less than one. We do that for a SIR/SEIR model, where infectious individuals have an infection age dependent infectivity, as in the model introduced in the 1927 seminal paper of Kermack and McKendrick. Our main conclusion is that simplifying the model as an ODE SIR model, as it is largely done in the epidemics literature, introduces a biais toward shorter extinction time.

math.PR↗

arXiv2020

A new approximation of the Height process of a CSBP

We code Galton-Walton trees by a continuous height process, in order to give a precise meaning to the convergence of forests of trees. This allows us to establish the convergence of the forest of genealogical trees of the branching process of a large population towards the genealogical trees of the limiting continuous state branching process (CSBP). The approximation considered here is new, compared to that which has been studied in Etienne Pardoux.

math.PR↗

arXiv2019

Approximation of the Height process of a CSBP with interaction

In this work, we first show that the properly rescaled height process of the genealogical tree of a continuous time branching process converges to the height process of the genealogy of a (possibly discontinuous) continuous state branching process. We then prove the same type of result for generalized branching processes with interaction.

math.PR↗

arXiv2017

Convergence to a Continuous State Branching Process with jumps and Height Process

In this work, we study asymptotics of the genealogy of Galton-Watson processes. Thus we consider a offspring distribution such that the rescaled Galton-Watson processes converges to a continuous state branching process (CSBP) with jumps. After we show that the rescaled height (or exploration) process of the corresponding Galton-Watson family tree, converges in a functional sense, to the continuous height process that Le Gall and Le Jan introduced in 1998 on their paper "branching processes in Lévy processes : The exploration process".

math.PR↗