Cervical cancer arises differentially from infections with up to 14 high-risk human papillomavirus (HPV) types, making model-based evaluations of cervical cancer screening strategies computationally heavy and structurally complex. Thus, with the high number of HPV types, microsimulation is typically used to investigate cervical cancer screening strategies. We developed a feasible deterministic model that integrates varying natural history of cervical cancer by the different high-risk HPV types with compressed mixture representations of the screened population, allowing for fast computation of screening interventions. To evaluate the method, we built a corresponding microsimulation model. The outcomes of the deterministic model were stable over different levels of compression and agreed with the microsimulation model for all disease states, screening outcomes, and levels of cancer incidence. The compression reduced the computation time more than 1000 fold when compared to microsimulation in a cohort of 1 million women. The compressed mixture representations enable the assessment of uncertainties surrounding the natural history of cervical cancer and screening decisions in a computationally undemanding way.