Cervical cancer, one of the deadliest diseases, is becoming a serious public health issue. In particular, developing countries face a significantly higher burden due to a lack of diagnostic and treatment facilities. In 2022, cervical cancer accounted for over 350,000 deaths and 660,000 new cases, making it the fourth most prevalent disease among women globally. Almost 94% of all deaths were reported in nations with low and middle incomes. Chronic infection with high-risk strains of the human papillomavirus (HPV) is the primary cause of this disease. The research developed a cervical cancer epidemic model to analyze the transmission dynamics of human papillomavirus (HPV) infection and the progression of cervical cancer. The existence, uniqueness, non-negativity, and boundedness of the model's solution are demonstrated. Two types of equilibrium points, disease-free equilibrium and endemic equilibrium, are calculated. The stability of both equilibrium points is also discussed. In order to identify the parameters that significantly contribute to the spread and persistence of the disease in the population, sensitivity indices are determined. Numerical simulation is performed through the Levenberg-Marquardt algorithm in conjunction with artificial neural networks (LM-ANNs), which support our analytical findings. The LM-ANNs' effectiveness, precision, reliability, validity, efficacy, accuracy, and convergence rate are evaluated through time series analysis, regression analysis, examination of the training state, evaluation of error histograms, convergence analysis, and the calculation of both absolute errors and statistical metrics. The numerical results are supported by analytical results.