In this talk we consider a two-level branching model for virus populations under cell division. We assume that the cells are carrying  a virus  which evolve as a continuous state branching processes with competition. The cells split binary according to a Yule process thereby dividing their virus populations into the two new cells. We then assume that sizes of the virus populations are huge and characterize the fast branching rate and huge population density limit as the solution of a well-posed martingale problem. While verifying tightness is quite standard, we present a Feynman-Kac duality relation to conclude uniqueness. This duality relation allows to find conditions under which the virus load of a typical cell stabilizes or tends to zero. (joint work with Luis Osorio)