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.
This work was partially funded by the Chair “Modélisation Mathématique et Biodiversité” of VEOLIA-Ecole Polytechnique-MNHN-F.X. and by the French national research agency (ANR) via project MEMIP (ANR-16-CE33-0018) and project NOLO (ANR-20-CE40-0015).
The authors are grateful to V. Bansaye for his advice and comments and to B. Cloez for fruitful discussions. They also want to thank the two anonymous referees for several corrections and improvements.
"Long time behaviour of continuous-state nonlinear branching processes with catastrophes." Electron. J. Probab. 26 1 - 32, 2021. https://doi.org/10.1214/21-EJP664