Worldwide, cervical cancer holds the fourth position in terms of prevalence among women, but for India, it is more severe holding the second position across the globe. The majority cases of this disease are exclusively linked with Human Papillomavirus (HPV). In most cases, cervical cancer presents no symptoms, leading to its detection at an advanced stage and resulting in death. Early detection of precancerous changes in infected cervical cells through screening programs helps facilitate timely intervention and treatment. Considering the screening program to be time-dependent, we have developed a four-dimensional mathematical model for cervical cancer prevention. This model provides a realistic mathematical framework about how the screening programs contribute to the reduction of cervical cancer cases. We have checked the positivity and boundedness of our proposed system, determined the basic reproduction number ( \(R_0\) ) to analyze the stability of the disease-free state, explored the existence condition of endemic equilibrium points, and furthermore, analyzed the stability of the infected steady state. We have validated all the obtained mathematical findings through numerical simulations in MATLAB 2016a.