Different types of mathematical models can be used to forecast the development of diseases as well as associated costs and analyse the cost-effectiveness of interventions. The set of models available to assess these parameters, reach from simple independent equations to highly complex agent-based simulations. For many diseases, it is simple to distinguish between infectious diseases and chronic-degenerative diseases. For infectious diseases, dynamic models are most appropriate because they allow for feedback from the number of infected to the number of new infections, while for the latter Markov models are more appropriate since this feedback is not required. However, for some diseases, the aforementioned distinction is not as clear. Cervical cancer, for instance, is caused by a sexually transmitted virus, and therefore falls under the definition of an infectious disease. However, once infected, the condition can progress to a chronic disease. Consequently, cervical cancer could be considered an infectious or a chronic-degenerative disease, depending on the stage of infection. In this paper, we will analyse the applicability of different mathematical models for epidemiological and economic processes focusing on cervical cancer. For this purpose, we will present the basic structure of different models. We will then conduct a literature analysis of the mathematical models used to predict the spread of cervical cancer. Based on these findings we will draw conclusions about which models can be used for which purpose and which disease. We conclude that each type of model has its advantages and disadvantages, but the choice of model type often seems arbitrary. In the case of cervical cancer, homogenous Markov models seem appropriate if a cohort of newly infected is followed for a shorter period, for instance, to assess the impact of screening programs. For long-term consequences, such as the impact of a vaccination program, a feedback loop from former infections to the future likelihood of infections is required. This can be done using system dynamics or inhomogeneous Markov models. Discrete event or agent-based simulations can be used in the case of cervical cancer when small cohorts or specific characteristics of individuals are required. However, these models require more effort than Markov or System Dynamics models.
