where f dec is the level of host translation factors at time t, relative to that of the initial state of the cell before infection (at t ¼ 0), and k d,host is the decay rate constant. The inhibition by the leader mRNA causes a first-order decay of the host factors, resulting in a shortage of the ribosomes equipped with the accessory factors for viral translation in the late infection stage in our model. Unlike viral transcription and replication, viral translation is directly affected by the decay of host factors since it depends entirely on host machinery. In the early infection, host mRNAs outnumber viral mRNAs and thereby successfully compete for the host translation machinery. However, the newly synthesized M proteins inhibit the host transcription initiation and the export of host mRNAs from the nucleus to the cytoplasm [57] , thereby causing a gradual shift in translation from host mRNAs to viral mRNAs. For our model we assumed that the potency of the inhibition by the M protein was independent of the type of cell and its differentiation state [36] , and we developed an empirical formula using available experimental data from the literature [36] to account for the competition between host and viral mRNAs for ribosomes. Lyles at al. cotransfected the host cells with VSV M mRNA and chloramphenicol acetyl transferase (CAT) plasmid DNA, and then they quantified the expression of CAT based on its activity, as a function of the expression of VSV M protein [36] . In their experiment the gene expression of CAT was more reduced at higher M protein expression levels. We assume that the decrease of the expression of CAT (or its activity decrease) is proportional to the decrease of the occupancy of host mRNAs by the translation machinery. Using their experimental data, the occupancy of host mRNAs by the translation machinery is correlated with the number of newly synthesized M proteins in the cytoplasm: