  The problem of modifying a network topology in such a way as to delay the
propagation of a disease with minimal disruption of the network capacity to
reroute goods/items/passengers is considered here. We find an approximate
solution to the Susceptible-Infected-Susceptible (SIS) model, which constitutes
a tight upper bound to its exact solution. This upper bound allows direct
structure-epidemic dynamic relations via the total communicability function.
Using this approach we propose a strategy to remove edges in a network that
significantly delays the propagation of a disease across the network with
minimal disruption of its capacity to deliver goods/items/passengers. We apply
this strategy to the analysis of the U.K. airport transportation network
weighted by the number of passengers transported in the year 2003. We find that
the removal of all flights connecting four origin-destination pairs in the U.K.
delays the propagation of a disease by more than 300\%, with a minimal
deterioration of the transportation capacity of this network. These time delays
in the propagation of a disease represent an important non-pharmaceutical
intervention to confront an epidemics, allowing for better preparations of the
health systems, while keeping the economy moving with minimal disruptions.
