The process of revitalising quiescent cells in order for them to proliferate plays a pivotalrole in the repair of worn-out tissues as well as for tissue homeostasis. This process is also crucialin the growth, development and well-being of higher multi-cellular organisms such as mammals.Deregulation of proliferation-quiescence transition is related to many diseases, such as cancer. Recentstudies have revealed that this proliferation–quiescence process is regulated tightly by the Rb − E2Fbistable switch mechanism. Based on experimental observations, in this study, we formulate amathematical model to examine the effect of the growth factor concentration on the proliferation–quiescence transition in human cells. Working with a non-dimensionalised model, we prove thepositivity, boundedness and uniqueness of solutions. To understand model solution behaviour closeto bifurcation points, we carry out bifurcation analysis, which is further illustrated by the use ofnumerical bifurcation analysis, sensitivity analysis and numerical simulations. Indeed, bifurcationand numerical analysis of the model predicted a transition between bistable and stable states, whichare dependent on the growth factor concentration parameter (GF). The derived predictions confirmexperimental observations.