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Epidemiological models describing the spread of infectious diseases within a population are fundamental to enable the design of control approaches that optimally curb the contagion, while coping with uncertainty in the parameter values. In the first part of the talk, we consider epidemic models formed by a positive compartmental system that includes various infected categories (e.g. asymptomatic, symptomatic, quarantined), fed back by a positive interaction representing contagion. Techniques from optimal and robust control theory allow us to assess the sensitivity of the model to uncertain parameter values. We also formulate an optimal control problem on a finite horizon and we discuss the peculiarities of its solution that, given the structure of the model, can be obtained in one iteration, without resorting to shooting procedures. On an infinite horizon, we show that the Hamilton-Jacobi-Bellman equation can be solved exactly. In the second part of the talk, we consider a general class of epidemic models with an arbitrary number of infected and non-infected (e.g. susceptible, vaccinated) compartments and we formulate an optimal vaccination control problem to minimize the number of infections and the cost of vaccination. We show that the sequential quadratic Hamiltonian (SQH) scheme, for which we offer rigorous global convergence guarantees, can solve the problem efficiently. As a main case study, we consider the dynamics of the COVID-19 pandemic, captured by the SIDARTHE model and its extensions.