High risk human papillomavirus (HPV) can induce cervical and oropharyngeal cancerous lesions. Different HPV strains, as well as still unknown mechanisms can be associated to a range of biochemical parameters that can importantly affect the HPV gene expression dynamics. For this reason, it is of pivotal importance to investigate how parameters variation can induce interesting behaviors such as viral latency in place of the normal gene replication activity. The aim of this study is to perform bifurcation analysis on a minimal model of the early promoter regulatory core controlled by E2 transcriptional regulation. The bifurcation analysis showed how E2 regulation can induce a bistability on the early promoter gene expression that could explain the interplay between viral latency and gene replication regimen.