Long time behaviour of continuous-state nonlinear branching processes with catastrophes

Aline Marguet (1) , Charline Smadi (2)

1 IBIS - Modeling, simulation, measurement, and control of bacterial regulatory networks
2 IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture

Motivated by the study of a parasite infection in a cell line, we introduce a general class of Markov processes for the modelling of population dynamics. The population process evolves as a diffusion with positive jumps whose rate is a function of the population size. It also undergoes catastrophic events which kill a fraction of the population, at a rate depending on the population state. We study the long time behaviour of this class of processes.

Mots clés: Continuous-time and space branching Markov processes; jumps; long time behaviour; absorption; explosion

Domaines: Probabilités [math.PR]

Aline Marguet, Charline Smadi. Long time behaviour of continuous-state nonlinear branching processes with catastrophes. 2020. ⟨hal-02274642v2⟩