Cell contamination and branching process in random environment with immigration

TL;DR

This paper models parasite infection dynamics in dividing cells using a branching process in a random environment with state-dependent immigration, analyzing long-term behavior and infection proportions.

Contribution

It introduces a novel branching process model incorporating contamination and state-dependent parasite sharing, with asymptotic analysis of parasite counts.

Findings

Asymptotic behavior of parasite numbers in cell lines determined.

Law of large numbers for proportions of infected cells established.

Model provides insights into infection spread in cell populations.

Abstract

We consider a branching model for a population of dividing cells infected by parasites. Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the population. Parasites multiply randomly inside the cell and are shared randomly between the two daughter cells when the cell divides. The law of the number of parasites which contaminate a given cell depends only on whether the cell is already infected or not. We determine the asymptotic behavior of the number of parasites in a cell line, which follows a branching process in random environment with state dependent immigration. We then derive a law of large numbers for the asymptotic proportions of cells with a given number of parasites. The main tools are branching processes in random environment and laws of large numbers for Markov tree.