  The aim of this paper is twofold. On one hand, we strive to give a simpler
proof of the optimality of greedy controls when the cost of interventions is
control-affine and the dynamics follow a state-constrained controlled SIR
model. This is achieved using the Hamilton-Jacobi characterization of the value
function, via the verification argument and explicit trajectorybased
computations. Aside from providing an alternative to the Pontryagin complex
arguments in [5], this method allows one to consider more general classes of
costs; in particular statedependent ones. On the other hand, the paper is
completed by linear programming methods allowing to deal with possibly
discontinuous costs. In particular, we propose a brief exposition of classes of
linearized dynamic programming principles based on our previous work and
ensuing dual linear programming algorithms. We emphasize the particularities of
our state space and possible generations of forward scenarios using the
description of reachable sets.
