Optimal Control of General Nonlocal Epidemic Models with Age and Space Structure

We analyze a class of general nonlinear epidemic models with age and space structure, including a nonlocal infection term depending on age and space. After establishing the well-posedness of the state partial differential equation, we introduce a control parameter interpreted as a vaccination rate. Under certain conditions, we show that an optimal control exists and how it can be characterized by first-order optimality conditions. Finally, we present numerical examples of the optimal control problems governed by these models.