The L∞/L1 duality in optimal control problems consists in studying how to link solutions minimizing the L∞ norm of an output function under an upper L1 constraint on an input function (primal problem), with solutions minimizing the L1 norm of the input function under an upper L∞ constraint on the output function (dual problem). In this work, we bring insights on recent results on L∞/L1 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.