Parasite infection in a cell population with deaths and reinfections.

We introduce a model of parasite infection in a cell population, where cells can be infected, either at birth through maternal transmission, from a contact with the parasites reservoir, or because of the parasites released in the cell medium after the lyses of infected cells. Inside the cells and between infection events, the quantity of parasites evolves as a general non linear branching process. We study the long time behaviour of the infection.