  We show we can control an epidemic reaction-diffusion on a directed, and
heterogeneous, network by redirecting the flows, thanks to the optimisation of
well-designed loss functions, in particular the basic reproduction number of
the model. We provide a final size relation linking the basic reproduction
number to the epidemic final sizes, for diffusions around a reference diffusion
with basic reproduction number less than 1. Experimentally, we show control is
possible for different topologies, network heterogeneity levels, and speeds of
diffusion. Our experimental results highlight the relevance of the basic
reproduction number loss, compared to more straightforward losses.
