Compartmental Models and Uncertainty Quantification in Epidemiology

Smoking is a major public health problem in the world. It is a leading cause of preventable diseases, including lung cancer, heart diseases, and respiratory problems. Efforts to combat smoking include awareness campaigns, stricter regulations, and support for cessation programs. The main goal of this dissertation is to produce a model for simulating the evolution of smoking habits in Tuscany, a region of central Italy, which can be easily adapted to other contexts. The developed model is based on a system of differential equations. These particular types of models in epidemiology are called compartmental models and are widely used for understanding dynamic population phenomena. Their mechanistic nature allows us to straightforwardly predict the evolution of a phenomenon by simulating its dynamic under different scenarios. However, the enormous complexity of these models makes the definition of the underlying likelihood function very difficult. For this reason in this thesis, we also present an overview of the suitable estimation methods for compartmental models, emphasizing the relevance of likelihood-free methods. Another important limitation due to the complexity of these models is given by the high uncertainty of the results and the difficulties in quantifying them. In this thesis, through the use of Global Sensitivity Analysis, we produce a robustification of the inference resulting from our model and conclude that the assumptions underlying our model are reasonable. Furthermore, we were able to assess the impact, in terms of the actual effectiveness, of implementing hypothetical tobacco control policies in Tuscany. As a conclusion to this thesis, we trace the evolution of sensitivity analysis over the years and assess its possible future progress.