This paper is devoted to the study of persistence and evolution of two viruses taking into account virus mutation, reproduction, and genotype dependent mortality, either natural or determined by an antiviral treatment. The model describes the virus density distribution u ( x ; t ) for the first virus and v(y; t ) for the second one as functions of genotypes x and y considered as continuous variables and of time t. The model consists of a system of reaction-diffusion equations with integral terms characterizing virus competition for host cells. The analysis of the model shows the conditions of the existence of virus strains.