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Abstract Viruses persist in nature owing to their extreme genetic heterogeneity and large –population sizes, which enable them to evade host immune defenses, escape anti-viral drugs, and adapt to new hosts. The persistence of viruses is challenging to study because mutations affect multiple virus genes, interactions among genes in their impacts on virus growth are seldom known, and measures of viral fitness have yet to be standardized. To address these challenges, we employed a data-driven computational model of cell infection by a virus. The infection model accounted for the kinetics of viral gene expression, functional gene-gene interactions, genome replication, and allocation of host cellular resources to produce progeny of vesicular stomatitis virus (VSV), a prototype RNA virus. We used this model to computationally probe how interactions among genes carrying up to 11 deleterious mutations affect different measures of virus fitness: single-cycle growth yields and multi-cycle rates of infection spread. Individual mutations were implemented by perturbing biophysical parameters associated with individual gene functions of the wild-type model. Our analysis revealed synergistic epistasis among deleterious mutations in their effects on virus yield; so adverse effects of single deleterious mutations were amplified by interaction. For the same mutations, multi-cycle infection spread indicated weak or negligible epistasis, where single mutations act alone in their effects on infection spread. These results were robust to simulation under high and low host resource environments. Our work highlights how different types and magnitudes of epistasis can arise for genetically identical virus variants, depending on the fitness measure. More broadly, gene-gene interactions can differently affect how viruses grow and spread.