Further results about L∞/L1 duality and applications to the SIR epidemiological model

The $L^{\infty} / L^{1}$ duality in optimal control problems consists in studying how to link solutions minimizing the $L^{\infty}$ norm of an output function under an upper $L^{1}$ constraint on an input function (primal problem), with solutions minimizing the $L^{1}$ norm of the input function under an upper $L^{\infty}$ constraint on the output function (dual problem). In this work, we bring insights on recent results on $L^{\infty} / L^{1}$ duality in optimal control problems. In particular, we exhibit an example for which duality does not apply, and we revisit the application to the epidemiological SIR problem.