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In this paper we study a two-level branching model for virus populationsunder cell division. We assume that the cells are carrying virus populationswhich evolve as a branching particle system with competition, while the cellssplit according to a Yule process thereby dividing their virus populations intotwo independently evolving sub-populations.  We then assume that sizes of the virus populations are huge and characterizethe fast branching rate and huge population density limit as the solution of awell-posed martingale problem. While verifying tightness is quite standard, weprovide a Feynman-Kac duality relation to conclude uniqueness. Moreover, theduality relation allows for a further study of the long term behavior of themodel.

Two level branching model for virus population under cell division