Parasite infection in a cell population with deaths

In this talk, I will introduce a general class of branching Markov processes for the modelling of a parasite infection in a cell population. Each cell contains a quantity of parasites which evolves as a diffusion with positive jumps. The growth rate, diffusive function and positive jump rate of this quantity of parasites depend on its current value. The division rate of the cells also depends on the quantity of parasites they contain. At division, a cell gives birth to two daughter cells and shares its parasites between them. Cells may also die, at a rate which may depend on the quantity of parasites they contain. Then, I will discuss the long time behaviour of the parasite infection, with a focus on the influence of two parameters on the probability for the cell population to survive: the law of the sharing of the parasites between the daughter cells at division and the form of the division and death rates of the cells as functions of the quantity of parasites they contain.
This work has been done in collaboration with Charline Smadi.