HPV infection starts with the activation of the early promoter (EP) regulatory core and the replication of the viral particles to around 10-100 per cell at the beginning of the infection. For this reason, understanding the deterministic and stochastic role of the population number of viruses inside the cell is of pivotal importance to understand the regulation of the EP and the viral latency.The aim of this study is to extend a recently published minimal model of the EP transcriptional regulation in order to consider the effect of the viral population on gene regulation, to perform the bifurcation analysis and to understand the role of the stochasticity at the beginning of the infection.The bifurcation analysis showed how modeling the viral population number is pivotal to exhibit a bistable behavior, potentially linked to the viral latency. Moreover, the viral population number was identified as an important source of stochasticity, which is of paramount importance to drive the bistable switching mechanism in the first stages of infection.