Sequential-Quadratic-Hamiltonian Optimal Control of Epidemic Models With an Arbitrary Number of Infected and Non-Infected Compartments

For a general class of epidemiological models with an arbitrary number of infected and non-infected compartments, we formulate an optimal vaccination control problem to minimize the number of infections and the cost of vaccination. We show that the problem can be solved efficiently with the sequential quadratic Hamiltonian (SQH) scheme, which we apply to the optimal control of epidemics for the first time and for which we prove rigorous global convergence guarantees in the case of a smooth cost functional. Our numerical simulations show that SQH outperforms the current state-of-the-art numerical scheme in mathematical epidemiology: its convergence can be guaranteed regardless of the initialization, it is faster and it is also applicable when the cost functional is non-smooth.