The design of biomanufacturing platforms based on viral transduction and/or propagation poses significant challenges at the intersection between synthetic biology and process engineering. This paper introduces vitraPro, a software toolkit composed of a multiscale model and an efficient numeric technique that can be leveraged for determining genetic and process designs that optimize transduction-based biomanufacturing platforms and viral amplification processes. Viral infection and propagation for up to two viruses simultaneously can be simulated through the model, considering viruses in either the lytic or lysogenic stage, during batch, perfusion, or continuous operation. The model estimates the distribution of the viral genome(s) copy number in the cell population, which is an indicator of transduction efficiency and viral genome stability. The infection age distribution of the infected cells is also calculated, indicating how many cells are in an infection stage compatible with recombinant product expression or viral amplification. The model can also consider the presence of defective interfering particles in the system, which can severely compromise the productivity of biomanufacturing processes. Model benchmarking and validation are demonstrated for case studies of the baculovirus expression vector system and influenza A propagation in suspension cultures.