A large group of biopharmaceuticals is produced in cell lines. The yield of such products can be increased by genetic engineering of the corresponding cell lines. The prediction of promising genetic modifications by mathematical modeling is a valuable tool to facilitate experimental screening. Besides information on the intracellular kinetics and genetic modifications the mathematical model has to account for ubiquitous cell-to-cell variability. In this contribution, we establish a novel model-based methodology for influenza vaccine production in cell lines with overexpressed genes. The manipulation of the expression level of genes coding for host cell factors relevant for virus replication is achieved by lentiviral transduction. Since lentiviral transduction causes increased cell-to-cell variability due to different copy numbers and integration sites of the gene constructs we use a population balance modeling approach to account for this heterogeneity in terms of intracellular viral components and distributed kinetic parameters. The latter are estimated from experimental data of intracellular viral RNA levels and virus titers of infection experiments using cells overexpressing a single host cell gene. For experiments with cells overexpressing multiple host cell genes, only final virus titers were measured and thus, no direct estimation of the parameter distributions was possible. Instead, we evaluate four different computational strategies to infer these from single gene parameter sets. Finally, the best computational strategy is used to predict the most promising candidates for future modifications that show the highest potential for an increased virus yield in a combinatorial study. As expected, there is a trend to higher yields the more modifications are included.