Herpes-Simplex Virus 1 (HSV-1) infects most humans when they are young, sometimes with fatal consequences. Gene expression occurs in a temporal order upon lytic HSV-1 infection: immediate early (IE) genes are expressed, then early (E) genes, followed by late (L) genes. During this infection cycle, the HSV-1 genome has the potential for exposure to APOBEC3 (A3) proteins, a family of cytidine deaminases that cause C>U mutations on single-stranded DNA (ssDNA), often resulting in a C>T transition. We developed a computational model for the mutational pressure of A3 on the lytic cycle of HSV-1 to determine which viral kinetic gene class is most vulnerable to A3 mutations. Using in silico stochastic methods, we simulated the infectious cycle under varying intensities of A3 mutational pressure. We found that the IE and E genes are more vulnerable to A3 than L genes. We validated this model by analyzing the A3 evolutionary footprints in 25 HSV-1 isolates. We find that IE and E genes have evolved to underrepresent A3 hotspot motifs more so than L genes, consistent with greater selection pressure on IE and E genes. We extend this model to two-step infections, such as those of polyomavirus, and find that the same pattern holds for over 25 human Polyomavirus (HPyVs) genomes. Genes expressed earlier during infection are more vulnerable to mutations than those expressed later.