Branching Feller diffusion for cell division with parasite infection

TL;DR

This paper models the evolution of parasite quantities within dividing cells using a Feller diffusion process with random splits, analyzing conditions for infection recovery or proliferation in cell populations.

Contribution

It introduces a stochastic model combining Feller diffusion with cell division and provides criteria for infection outcomes in the population.

Findings

Derived asymptotic behavior of parasite quantity in a cell line.

Established criteria for infection recovery or proliferation.

Analyzed the impact of division rate on infection dynamics.

Abstract

We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when a division occurs. The cell division rate may depend on the quantity of parasites inside the cell and we are interested in the cases of constant or monotone division rate. We first determine the asymptotic behavior of the quantity of parasites in a cell line, which follows a Feller diffusion with multiplicative jumps. We then consider the evolution of the infection of the cell population and give criteria to determine whether the proportion of infected cells goes to zero (recovery) or if a positive proportion of cells becomes largely infected (proliferation of parasites inside the cells).