Emerging and existing infectious diseases pose a constant threat to individuals and communities across the world. In many cases, the burden of these diseases is preventable through public health interventions. However, taking the right decisions and designing effective policies is an intricate task: epidemics are complex phenomena resulting from the interaction between the environment, pathogens, individuals, and societies. Modeling offers a principled way to reason about infectious disease dynamics from scarce and biased information and to guide decision-makers towards effective policies.

This thesis tackles selected topics in cholera and COVID-19 modeling towards informed public-health decisions. These two contrasting diseases were associated by a twist of fate, but also through the lens of a common modeling approach: compartmental, SIR-based, models are conditioned on the available evidence using computer-age statistical inference frameworks. A set of five models is developed, each tackling a different facet of the spread and control of these two infectious diseases. Each model aims at answering questions related to either the understanding of the mechanisms behind disease transmission, the projection of the future dynamics under different scenarios, or the assessment of the effectiveness of past interventions. Moreover, a novel application of epidemiological models to the formal design of control policies is proposed. Optimal control provides a rigorous framework to identify the most effective control measures under a set of operational constraints, providing a benchmark on what it is possible to achieve with the available resources.

The results presented in this thesis range from scientific insight on the relationship between cholera and rainfall in Juba, South Sudan to the COVID Scenario Pipeline which produces reports used to inform the response to the COVID-19 pandemic of different governmental entities. Furthermore, the effectiveness of the non-pharmaceutical interventions against COVID-19 in Switzerland is evaluated; and so is the probability of eliminating cholera from Haiti under different scenarios of mass vaccination campaigns. Finally, the development of an optimal control framework towards the effective spatial allocation of vaccines against SARS-CoV-2 in Italy closes this conversation of models.

The present thesis demonstrates how infectious disease modeling enables informed decision-making by projecting the uncertainties under the light of the available evidence. It also highlights the effort needed to tailor the models and inference methods to the specificities of the transmission setting and the research question considered. From insights on transmission pathways to weekly reports aimed at decision-makers, it explores different applications of infectious disease modeling. Methods developed along the way enrich the toolbox available to modelers, to guide policy decisions further towards a reduction of the burden of infectious diseases on communities.