  The authors study an infinite dimensional duality theory finalized to obtain
the existence of a strong duality between a convex optimization problem
connected with the management of vaccinations and its Lagrange dual.
Specifically, the authors show the solvability of a dual problem using as basic
tool an hypothesis known as Assumption S. Roughly speaking, it requires to show
that a particular limit is nonnegative. This technique improves the previous
strong duality results that need the nonemptyness of the interior of the convex
ordering cone. The authors use the duality theory to analyze the dynamic
vaccination game in order to obtain the existence of the Lagrange multipliers
related to the problem and to better comprehend the meaning of the problem.
