Multi-objective Design with a Stochastic Validation of Vaccination Campaigns*

The planning of vaccination campaigns should minimize two factors: the number of infected individuals in a time horizon and the cost to implement the control. This problem is stated here as a non-linear dynamic programming optimisation with impulsive control. The traditional SIR (Susceptible-Infected-Recovered) differential equation model is employed for representing the system, and the dynamic programming problem is solved in open-loop, leading to a static non-linear multi-objective optimisation problem. The NSGA-II, which is a standard multi-objective genetic algorithm, is employed as the optimisation machinery. A stochastic dynamic model of the epidemics is employed in order to validate the vaccination strategy, helping in the choice of the specific strategy to be implemented. The final result shows a set of interval of confidence for each optimal policy strategy.