During the last decades public health policy makers have been increasingly turning to mathematical modeling to support their decisions. This trend has been calling for the introduction of a new class of models that not only are capable to explain qualitatively the dynamics of infectious diseases, but also have the capability to provide quantitatively reliable and accurate results. To this aim models are becoming more and more detailed and informed with data. However, there is still much to be done in order to capture the individual and population features that shape the spread of infectious diseases. This thesis addresses some issues in epidemiological modeling that warrant further investigation. In Chapter 1 we introduce an age-structured individual-based stochastic model of Varicella Zoster Virus (VZV) transmission, whose main novelty is the inclusion of realistic population dynamics over the last century. This chapter represents an attempt to answer the need pointed out by recent studies for a better understanding of the role of demographic processes in shaping the circulation of infectious diseases. In Chapter 2 we use the model for VZV transmission developed in Chapter 1 to evaluate the effectiveness of varicella and HZ vaccination programs in Italy. With a view to the support of public health decisions, the epidemiological model is coupled with a cost-effectiveness analysis. To the best of our knowledge, this work represents the first attempt to evaluate the post-vaccination trends in varicella and HZ, both from an epidemiological and economic perspective, in light of the underlying effect of demographic processes. Another novelty of this study is that we take into account the uncertainty regarding the mechanism of VZV reactivation, by comparing results obtained using two different modeling assumptions on exogenous boosting. In Chapter 3 we retrospectively analyze the spatiotemporal dynamics of the 2009 H1N1 influenza pandemic in England, by using a spatially-explicit model of influenza transmission, accounting for socio-demographic and disease natural history data. The aim of this work is to investigate whether the observed spatiotemporal dynamics of the epidemic was shaped by a spontaneous behavioral response to the pandemic threat. This chapter, represents an attempt to contribute to the challenge of understanding and quantifying the effect of human behavioral changes on the spread of epidemics. In Chapter 4 we investigate the current epidemiology of measles in Italy, by using a detailed computational model for measles transmission, informed with regional heterogeneities in the age-specific seroprevalence profiles. The analysis performed in this chapter tries to fill some of the existing gaps in the knowledge of the epidemiological features of vaccine preventable diseases in frameworks characterized by a low circulation of the virus.

The works presented in this thesis are very different one from the other but they all deal with the mathematical modelling of emerging infectious diseases which, beyond being the leitmotiv of this thesis, is an important research area in the field of epidemiology and public health. A minor but significant part of the thesis has a theoretical flavour. This part is dedicated to the mathematical analysis of the competition model between two HIV subtypes in presence of vaccination and cross-immunity proposed by Porco and Blower (1998). We find the sharp conditions under which vaccination leads to the coexistence of the strains and using arguments from bifurcation theory, draw conclusions on the equilibria stability and find that a rather unusual behaviour of histeresis-type might emerge after repeated variations of the vaccination rate within a certain range. The most of this thesis has been inspired by real outbreaks occurred in Italy over the last 10 years and is about the modelling of the 1999-2000 H7N1 avian influenza outbreak and of the 2009-2010 H1N1 pandemic influenza. From an applied perspective, parameter estimation is a key part of the modelling process and in this thesis statistical inference has been performed within both a classical framework (i.e. by maximum likelihood and least square methods) and a Bayesian setting (i.e. by Markov Chain Monte Carlo techniques). However, my contribution goes beyond the application of inferential techniques to specific case studies. The stochastic, spatially explicit, between-farm transmission model developed for the transmission of the H7N1 virus has indeed been used to simulate different control strategies and asses their relative effectiveness. The modelling framework presented here for the H1N1 pandemic in Italy constitutes a novel approach that can be applied to a variety of different infections detected by surveillance system in many countries. We have coupled a deterministic compartmental model with a statistical description of the reporting process and have taken into account for the presence of stochasticity in the surveillance system. We thus tackled some statistical challenging issues (such as the estimation of the fraction of H1N1 cases reporting influenza-like-illness symptoms) that had not been addressed before. Last, we apply different estimation methods usually adopted in epidemiology to real and simulated school outbreaks, in the attempt to explore the suitability of a specific individual-based model at reproducing empirically observed epidemics in specific social contexts.